Determine the area bounded by g(x) = x– 4x +7 and h(x) = x + 5.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1.
Determine the area bounded by g(x) = x3- 4x +7 and h(x) = x + 5.
2. Find the larger area formed by x2 + 3y2 + 7x = 3 and 2x2 – 6y = 5.
3. Find the area intercepted by the three equations 4x2 – y2 + 2x = 1, y? – x = 4, and y = x- 2.
4. Solve for the area common with r 2+5 cos(20) and r= 5 sin(0).
5. Find the total area between r = 4 sin(0) and r =
7 sin(40).
6. Determine the volume if the area common with y2 - 3x + 7y 8 and x² – 4x + 3 = y² is revolved about the
directrix of the given parabola.
7. A solid dome is to be constructed with the ellipse x2 +3y2 = 6 as a base. Using infinitely many semi-cirdles,
determine the volume that this solid will generate.
8. Find the arc length of y3 + y = x2 + 6x on the interval [-5,-1].
9. Using the same arc in number 8, determine the surface of revolution if it is revolved about y = -3.
10. Given the expression x- 3x + 7 = y3 on the interval [3,5], determine the surface of revolution if it is revolved
about x = -3.
Transcribed Image Text:1. Determine the area bounded by g(x) = x3- 4x +7 and h(x) = x + 5. 2. Find the larger area formed by x2 + 3y2 + 7x = 3 and 2x2 – 6y = 5. 3. Find the area intercepted by the three equations 4x2 – y2 + 2x = 1, y? – x = 4, and y = x- 2. 4. Solve for the area common with r 2+5 cos(20) and r= 5 sin(0). 5. Find the total area between r = 4 sin(0) and r = 7 sin(40). 6. Determine the volume if the area common with y2 - 3x + 7y 8 and x² – 4x + 3 = y² is revolved about the directrix of the given parabola. 7. A solid dome is to be constructed with the ellipse x2 +3y2 = 6 as a base. Using infinitely many semi-cirdles, determine the volume that this solid will generate. 8. Find the arc length of y3 + y = x2 + 6x on the interval [-5,-1]. 9. Using the same arc in number 8, determine the surface of revolution if it is revolved about y = -3. 10. Given the expression x- 3x + 7 = y3 on the interval [3,5], determine the surface of revolution if it is revolved about x = -3.
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