Explanation Given: The intgeral is ∫ d x 12 x − x 2 . Key concept used: Steps of integration by substitution: If the integral is in the below form: ∫ f ( g ( x ) ) g ′ ( x ) d x Let u = g ( x ) and d u = g ′ ( x ) d x The intgeral becomes, ∫ f ( u ) d u . Thus, integrate f ( u ) . After that substitute g ( x ) back. Trigonometic formula: cos 2 x = 1 − sin 2 x Integration formula: ∫ 1 d x = x + c Calculation: The intgeral is ∫ d x 12 x − x 2 . We can rewrite the integral as: ∫ d x 12 x − x 2 = ∫ d x 36 − ( x − 6 ) 2 ... (1) Let x − 6 = 6 sin θ . Now, differentiate x − 6 = 6 sin θ . d x = 6 cos θ d θ Substitute 6 sin θ for x − 6 and 6 cos θ d θ for d x in equation (1)...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Videos

Question

Chapter 8.3, Problem 38E

To determine

Evaluate the integral $\int \frac{d x}{\sqrt{12 x - x^{2}}}$ . First, complete the square to write $12 x - x^{2} = 36 - {(x - 6)}^{2}$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 37E

Chapter 8.3, Problem 39E

Chapter 8 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - Prob. 61E Ch. 8.1 - Prob. 62E Ch. 8.1 - Prob. 63E Ch. 8.1 - Prob. 64E Ch. 8.1 - Prob. 65E Ch. 8.1 - Prob. 66E Ch. 8.1 - Prob. 67E Ch. 8.1 - Prob. 68E Ch. 8.1 - Prob. 69E Ch. 8.1 - Prob. 70E Ch. 8.1 - Prob. 71E Ch. 8.1 - Prob. 72E Ch. 8.1 - Prob. 73E Ch. 8.1 - Prob. 74E Ch. 8.1 - Prob. 75E Ch. 8.1 - Prob. 76E Ch. 8.1 - Prob. 77E Ch. 8.1 - Prob. 78E Ch. 8.1 - Prob. 79E Ch. 8.1 - Prob. 80E Ch. 8.1 - Prob. 81E Ch. 8.1 - Prob. 82E Ch. 8.1 - Prob. 83E Ch. 8.1 - Prob. 84E Ch. 8.1 - Prob. 85E Ch. 8.1 - Prob. 86E Ch. 8.1 - Prob. 87E Ch. 8.1 - Prob. 88E Ch. 8.1 - Prob. 89E Ch. 8.1 - Prob. 90E Ch. 8.1 - Prob. 91E Ch. 8.1 - Prob. 92E Ch. 8.1 - Prob. 93E Ch. 8.1 - Prob. 94E Ch. 8.1 - Prob. 95E Ch. 8.1 - Prob. 96E Ch. 8.1 - Prob. 97E Ch. 8.2 - Prob. 1PQ Ch. 8.2 - Prob. 2PQ Ch. 8.2 - Prob. 3PQ Ch. 8.2 - Prob. 4PQ Ch. 8.2 - Prob. 5PQ Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55E Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.2 - Prob. 59E Ch. 8.2 - Prob. 60E Ch. 8.2 - Prob. 61E Ch. 8.2 - Prob. 62E Ch. 8.2 - Prob. 63E Ch. 8.2 - Prob. 64E Ch. 8.2 - Prob. 65E Ch. 8.2 - Prob. 66E Ch. 8.2 - Prob. 67E Ch. 8.2 - Prob. 68E Ch. 8.2 - Prob. 69E Ch. 8.2 - Prob. 70E Ch. 8.2 - Prob. 71E Ch. 8.2 - Prob. 72E Ch. 8.2 - Prob. 73E Ch. 8.2 - Prob. 74E Ch. 8.2 - Prob. 75E Ch. 8.2 - Prob. 76E Ch. 8.2 - Prob. 77E Ch. 8.3 - Prob. 1PQ Ch. 8.3 - Prob. 2PQ Ch. 8.3 - Prob. 3PQ Ch. 8.3 - Prob. 4PQ Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Prob. 44E Ch. 8.3 - Prob. 45E Ch. 8.3 - Prob. 46E Ch. 8.3 - Prob. 47E Ch. 8.3 - Prob. 48E Ch. 8.3 - Prob. 49E Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.3 - Prob. 52E Ch. 8.3 - Prob. 53E Ch. 8.3 - Prob. 54E Ch. 8.3 - Prob. 55E Ch. 8.3 - Prob. 56E Ch. 8.3 - Prob. 57E Ch. 8.4 - Prob. 1PQ Ch. 8.4 - Prob. 2PQ Ch. 8.4 - Prob. 3PQ Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - Prob. 42E Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 45E Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.4 - Prob. 48E Ch. 8.4 - Prob. 49E Ch. 8.4 - Prob. 50E Ch. 8.5 - Prob. 1PQ Ch. 8.5 - Prob. 2PQ Ch. 8.5 - Prob. 3PQ Ch. 8.5 - Prob. 4PQ Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - Prob. 5E Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - Prob. 12E Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Prob. 30E Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.5 - Prob. 38E Ch. 8.5 - Prob. 39E Ch. 8.5 - Prob. 40E Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Prob. 45E Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.5 - Prob. 57E Ch. 8.5 - Prob. 58E Ch. 8.5 - Prob. 59E Ch. 8.5 - Prob. 60E Ch. 8.5 - Prob. 61E Ch. 8.5 - Prob. 62E Ch. 8.6 - Prob. 1PQ Ch. 8.6 - Prob. 2PQ Ch. 8.6 - Prob. 3PQ Ch. 8.6 - Prob. 4PQ Ch. 8.6 - Prob. 5PQ Ch. 8.6 - Prob. 6PQ Ch. 8.6 - Prob. 7PQ Ch. 8.6 - Prob. 8PQ Ch. 8.6 - Prob. 9PQ Ch. 8.6 - Prob. 10PQ Ch. 8.6 - Prob. 11PQ Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Prob. 24E Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.6 - Prob. 37E Ch. 8.6 - Prob. 38E Ch. 8.6 - Prob. 39E Ch. 8.6 - Prob. 40E Ch. 8.6 - Prob. 41E Ch. 8.6 - Prob. 42E Ch. 8.6 - Prob. 43E Ch. 8.6 - Prob. 44E Ch. 8.6 - Prob. 45E Ch. 8.6 - Prob. 46E Ch. 8.6 - Prob. 47E Ch. 8.6 - Prob. 48E Ch. 8.6 - Prob. 49E Ch. 8.6 - Prob. 50E Ch. 8.6 - Prob. 51E Ch. 8.6 - Prob. 52E Ch. 8.6 - Prob. 53E Ch. 8.6 - Prob. 54E Ch. 8.6 - Prob. 55E Ch. 8.6 - Prob. 56E Ch. 8.6 - Prob. 57E Ch. 8.6 - Prob. 58E Ch. 8.6 - Prob. 59E Ch. 8.6 - Prob. 60E Ch. 8.7 - Prob. 1PQ Ch. 8.7 - Prob. 2PQ Ch. 8.7 - Prob. 3PQ Ch. 8.7 - Prob. 4PQ Ch. 8.7 - Prob. 5PQ Ch. 8.7 - Prob. 1E Ch. 8.7 - Prob. 2E Ch. 8.7 - Prob. 3E Ch. 8.7 - Prob. 4E Ch. 8.7 - Prob. 5E Ch. 8.7 - Prob. 6E Ch. 8.7 - Prob. 7E Ch. 8.7 - Prob. 8E Ch. 8.7 - Prob. 9E Ch. 8.7 - Prob. 10E Ch. 8.7 - Prob. 11E Ch. 8.7 - Prob. 12E Ch. 8.7 - Prob. 13E Ch. 8.7 - Prob. 14E Ch. 8.7 - Prob. 15E Ch. 8.7 - Prob. 16E Ch. 8.7 - Prob. 17E Ch. 8.7 - Prob. 18E Ch. 8.7 - Prob. 19E Ch. 8.7 - Prob. 20E Ch. 8.7 - Prob. 21E Ch. 8.7 - Prob. 22E Ch. 8.7 - Prob. 23E Ch. 8.7 - Prob. 24E Ch. 8.7 - Prob. 25E Ch. 8.7 - Prob. 26E Ch. 8.7 - Prob. 27E Ch. 8.7 - Prob. 28E Ch. 8.7 - Prob. 29E Ch. 8.7 - Prob. 30E Ch. 8.7 - Prob. 31E Ch. 8.7 - Prob. 32E Ch. 8.7 - Prob. 33E Ch. 8.7 - Prob. 34E Ch. 8.7 - Prob. 35E Ch. 8.7 - Prob. 36E Ch. 8.7 - Prob. 37E Ch. 8.7 - Prob. 38E Ch. 8.7 - Prob. 39E Ch. 8.7 - Prob. 40E Ch. 8.7 - Prob. 41E Ch. 8.7 - Prob. 42E Ch. 8.7 - Prob. 43E Ch. 8.7 - Prob. 44E Ch. 8.7 - Prob. 45E Ch. 8.7 - Prob. 46E Ch. 8.7 - Prob. 47E Ch. 8.7 - Prob. 48E Ch. 8.7 - Prob. 49E Ch. 8.7 - Prob. 50E Ch. 8.7 - Prob. 51E Ch. 8.7 - Prob. 52E Ch. 8.7 - Prob. 53E Ch. 8.7 - Prob. 54E Ch. 8.7 - Prob. 55E Ch. 8.7 - Prob. 56E Ch. 8.7 - Prob. 57E Ch. 8.7 - Prob. 58E Ch. 8.7 - Prob. 59E Ch. 8.7 - Prob. 60E Ch. 8.7 - Prob. 61E Ch. 8.7 - Prob. 62E Ch. 8.7 - Prob. 63E Ch. 8.7 - Prob. 64E Ch. 8.7 - Prob. 65E Ch. 8.7 - Prob. 66E Ch. 8.7 - Prob. 67E Ch. 8.7 - Prob. 68E Ch. 8.7 - Prob. 69E Ch. 8.7 - Prob. 70E Ch. 8.7 - Prob. 71E Ch. 8.7 - Prob. 72E Ch. 8.7 - Prob. 73E Ch. 8.7 - Prob. 74E Ch. 8.7 - Prob. 75E Ch. 8.7 - Prob. 76E Ch. 8.7 - Prob. 77E Ch. 8.7 - Prob. 78E Ch. 8.7 - Prob. 79E Ch. 8.7 - Prob. 80E Ch. 8.7 - Prob. 81E Ch. 8.7 - Prob. 82E Ch. 8.7 - Prob. 83E Ch. 8.7 - Prob. 84E Ch. 8.7 - Prob. 85E Ch. 8.7 - Prob. 86E Ch. 8.7 - Prob. 87E Ch. 8.7 - Prob. 88E Ch. 8.7 - Prob. 89E Ch. 8.7 - Prob. 90E Ch. 8.7 - Prob. 91E Ch. 8.7 - Prob. 92E Ch. 8.7 - Prob. 93E Ch. 8.7 - Prob. 94E Ch. 8.7 - Prob. 95E Ch. 8.7 - Prob. 96E Ch. 8.7 - Prob. 97E Ch. 8.7 - Prob. 98E Ch. 8.7 - Prob. 99E Ch. 8.7 - Prob. 100E Ch. 8.7 - Prob. 101E Ch. 8.7 - Prob. 102E Ch. 8.8 - Prob. 1PQ Ch. 8.8 - Prob. 2PQ Ch. 8.8 - Prob. 3PQ Ch. 8.8 - Prob. 4PQ Ch. 8.8 - Prob. 5PQ Ch. 8.8 - Prob. 1E Ch. 8.8 - Prob. 2E Ch. 8.8 - Prob. 3E Ch. 8.8 - Prob. 4E Ch. 8.8 - Prob. 5E Ch. 8.8 - Prob. 6E Ch. 8.8 - Prob. 7E Ch. 8.8 - Prob. 8E Ch. 8.8 - Prob. 9E Ch. 8.8 - Prob. 10E Ch. 8.8 - Prob. 11E Ch. 8.8 - Prob. 12E Ch. 8.8 - Prob. 13E Ch. 8.8 - Prob. 14E Ch. 8.8 - Prob. 15E Ch. 8.8 - Prob. 16E Ch. 8.8 - Prob. 17E Ch. 8.8 - Prob. 18E Ch. 8.8 - Prob. 19E Ch. 8.8 - Prob. 20E Ch. 8.8 - Prob. 21E Ch. 8.8 - Prob. 22E Ch. 8.8 - Prob. 23E Ch. 8.8 - Prob. 24E Ch. 8.8 - Prob. 25E Ch. 8.8 - Prob. 26E Ch. 8.8 - Prob. 27E Ch. 8.8 - Prob. 28E Ch. 8.8 - Prob. 29E Ch. 8.8 - Prob. 30E Ch. 8.8 - Prob. 31E Ch. 8.8 - Prob. 32E Ch. 8.8 - Prob. 33E Ch. 8.8 - Prob. 34E Ch. 8.8 - Prob. 35E Ch. 8.8 - Prob. 36E Ch. 8.8 - Prob. 37E Ch. 8.8 - Prob. 38E Ch. 8.8 - Prob. 39E Ch. 8.8 - Prob. 40E Ch. 8.8 - Prob. 41E Ch. 8.8 - Prob. 42E Ch. 8.8 - Prob. 43E Ch. 8.8 - Prob. 44E Ch. 8.8 - Prob. 45E Ch. 8.8 - Prob. 46E Ch. 8.8 - Prob. 47E Ch. 8.8 - Prob. 48E Ch. 8.8 - Prob. 49E Ch. 8.8 - Prob. 50E Ch. 8.8 - Prob. 51E Ch. 8.8 - Prob. 52E Ch. 8.8 - Prob. 53E Ch. 8.8 - Prob. 54E Ch. 8.8 - Prob. 55E Ch. 8.8 - Prob. 56E Ch. 8.8 - Prob. 57E Ch. 8.8 - Prob. 58E Ch. 8.8 - Prob. 59E Ch. 8.8 - Prob. 60E Ch. 8.8 - Prob. 61E Ch. 8.8 - Prob. 62E Ch. 8.8 - Prob. 63E Ch. 8.8 - Prob. 64E Ch. 8.8 - Prob. 65E Ch. 8.8 - Prob. 66E Ch. 8 - Prob. 1CRE Ch. 8 - Prob. 2CRE Ch. 8 - Prob. 3CRE Ch. 8 - Prob. 4CRE Ch. 8 - Prob. 5CRE Ch. 8 - Prob. 6CRE Ch. 8 - Prob. 7CRE Ch. 8 - Prob. 8CRE Ch. 8 - Prob. 9CRE Ch. 8 - Prob. 10CRE Ch. 8 - Prob. 11CRE Ch. 8 - Prob. 12CRE Ch. 8 - Prob. 13CRE Ch. 8 - Prob. 14CRE Ch. 8 - Prob. 15CRE Ch. 8 - Prob. 16CRE Ch. 8 - Prob. 17CRE Ch. 8 - Prob. 18CRE Ch. 8 - Prob. 19CRE Ch. 8 - Prob. 20CRE Ch. 8 - Prob. 21CRE Ch. 8 - Prob. 22CRE Ch. 8 - Prob. 23CRE Ch. 8 - Prob. 24CRE Ch. 8 - Prob. 25CRE Ch. 8 - Prob. 26CRE Ch. 8 - Prob. 27CRE Ch. 8 - Prob. 28CRE Ch. 8 - Prob. 29CRE Ch. 8 - Prob. 30CRE Ch. 8 - Prob. 31CRE Ch. 8 - Prob. 32CRE Ch. 8 - Prob. 33CRE Ch. 8 - Prob. 34CRE Ch. 8 - Prob. 35CRE Ch. 8 - Prob. 36CRE Ch. 8 - Prob. 37CRE Ch. 8 - Prob. 38CRE Ch. 8 - Prob. 39CRE Ch. 8 - Prob. 40CRE Ch. 8 - Prob. 41CRE Ch. 8 - Prob. 42CRE Ch. 8 - Prob. 43CRE Ch. 8 - Prob. 44CRE Ch. 8 - Prob. 45CRE Ch. 8 - Prob. 46CRE Ch. 8 - Prob. 47CRE Ch. 8 - Prob. 48CRE Ch. 8 - Prob. 49CRE Ch. 8 - Prob. 50CRE Ch. 8 - Prob. 51CRE Ch. 8 - Prob. 52CRE Ch. 8 - Prob. 53CRE Ch. 8 - Prob. 54CRE Ch. 8 - Prob. 55CRE Ch. 8 - Prob. 56CRE Ch. 8 - Prob. 57CRE Ch. 8 - Prob. 58CRE Ch. 8 - Prob. 59CRE Ch. 8 - Prob. 60CRE Ch. 8 - Prob. 61CRE Ch. 8 - Prob. 62CRE Ch. 8 - Prob. 63CRE Ch. 8 - Prob. 64CRE Ch. 8 - Prob. 65CRE Ch. 8 - Prob. 66CRE Ch. 8 - Prob. 67CRE Ch. 8 - Prob. 68CRE Ch. 8 - Prob. 69CRE Ch. 8 - Prob. 70CRE Ch. 8 - Prob. 71CRE Ch. 8 - Prob. 72CRE Ch. 8 - Prob. 73CRE Ch. 8 - Prob. 74CRE Ch. 8 - Prob. 75CRE Ch. 8 - Prob. 76CRE Ch. 8 - Prob. 77CRE Ch. 8 - Prob. 78CRE Ch. 8 - Prob. 79CRE Ch. 8 - Prob. 80CRE Ch. 8 - Prob. 81CRE Ch. 8 - Prob. 82CRE Ch. 8 - Prob. 83CRE Ch. 8 - Prob. 84CRE Ch. 8 - Prob. 85CRE Ch. 8 - Prob. 86CRE Ch. 8 - Prob. 87CRE Ch. 8 - Prob. 88CRE Ch. 8 - Prob. 89CRE Ch. 8 - Prob. 90CRE Ch. 8 - Prob. 91CRE Ch. 8 - Prob. 92CRE Ch. 8 - Prob. 93CRE Ch. 8 - Prob. 94CRE Ch. 8 - Prob. 95CRE Ch. 8 - Prob. 96CRE Ch. 8 - Prob. 97CRE Ch. 8 - Prob. 98CRE Ch. 8 - Prob. 99CRE Ch. 8 - Prob. 100CRE Ch. 8 - Prob. 101CRE Ch. 8 - Prob. 102CRE Ch. 8 - Prob. 103CRE Ch. 8 - Prob. 104CRE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Evaluate the integral ∫ d x 12 x − x 2 . First, complete the square to write 12 x − x 2 = 36 − ( x − 6 ) 2 .

Solution Summary: The author explains the steps of integration by substitution.

Concept explainers

Videos

Evaluate the integral $\int \frac{d x}{\sqrt{12 x - x^{2}}}$ . First, complete the square to write $12 x - x^{2} = 36 - {(x - 6)}^{2}$ .

Want to see the full answer?

Chapter 8 Solutions

Evaluate the integral ∫ d x 12 x − x 2 . First, complete the square to write 12 x − x 2 = 36 − ( x − 6 ) 2 .

Solution Summary: The author explains the steps of integration by substitution.

Concept explainers

Videos

Evaluate the integral ∫dx12x−x2. First, complete the square to write 12x−x2=36−(x−6)2.

Want to see the full answer?

Chapter 8 Solutions

Evaluate the integral $\int \frac{d x}{\sqrt{12 x - x^{2}}}$ . First, complete the square to write $12 x - x^{2} = 36 - {(x - 6)}^{2}$ .