In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent . 48. ∫ 3 x 2 ( x 3 + 1 ) d x
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent . 48. ∫ 3 x 2 ( x 3 + 1 ) d x
Solution Summary: The author calculates the value of the indefinite integral by substituting the substitution method and checking the answers are equivalent or not.
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
48.
∫
3
x
2
(
x
3
+
1
)
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Please, help me to solve problem num 41 step by steps.
Find the derivatives in Exercises 39–44.a. by evaluating the integral and differentiating the result. b. by differentiating the integral directly.
8
et
dt
7t
21.
sin(9x)
Solve.
1. Find the equation of the family of curves whose slope at any point (x, y) is 3x.
2. What will be the definite integral if you will get the integral of the equation x^2 + 2x from 0 to 2.
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY