Explanation Given: The equation of the curves are y = 1 + x 4 and y = 3 − x 3 . Calculation: The equation of the curves are as follows: y = 1 + x 4 (1) y = 3 − x 3 (2) Draw the graph for the function y = 1 + x 4 and y = 3 − x 3 by substituting different values for x . Sketch the region enclosed by the curves as shown below in Figure 1. From Figure 1, it is observed that the shaded region represents the region enclosed by the given curves. From the Figure 1, the intersection points are x = − 1 and x = 0.857 . Hence, the approximate x- coordinates of the point of intersection of the given curves are x = − 1 and x = 0.857 . Consider that the outer radius of the region r 1 = 3 − x 3 and the inner radius of the region r 2 = 1 + x 4 within the limit − 1 to 0.857 . Then the area enclosed by the curves is as shown below. A ( x ) = π r 1 2 − π r 2 2 = π ( 3 − x 3 ) 2 − π ( 1 + x 4 ) 2 = π ( 3 − x 3 − 1 − x 8 − 2 x 4 ) = π ( 2 − x 3 − x 8 − 2 x 4 ) Thus, the volume of the solid obtained by rotating about the x -axis is, V = ∫ a b A ( x ) d x (3) Substitute − 1 for a , 0.857 for b and π ( 2 − x 3 − x 8 − 2 x 4 ) for A ( x ) in Equation (3)

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Chapter 5.2, Problem 35E

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To find: The approximate x-coordinates of the point of intersection of the given curves and the volume of the solid obtained by rotating about the x-axis.

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Chapter 5.2, Problem 34E

Chapter 5.2, Problem 36E

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Chapter 5 Solutions

EBK SINGLE VARIABLE CALCULUS, VOLUME 1

Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 6E Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 8E Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....

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The approximate x- coordinates of the point of intersection of the given curves and the volume of the solid obtained by rotating about the x -axis.

Solution Summary: The author calculates the approximate x- coordinates of the point of intersection of given curves and the volume of solid obtained by rotating about the X -axis.

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To find: The approximate x-coordinates of the point of intersection of the given curves and the volume of the solid obtained by rotating about the x-axis.

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Chapter 5 Solutions