The region R is bounded by the curves x = y 2 + 2, y = x

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The region R is bounded by the curves x = y2 + 2, y = x - 4, and y = 0 (see figure).

a. Write a single integral that gives the area of R.

b. Write a single integral that gives the volume of the solid generated when R is revolved about the x-axis.

c. Write a single integral that gives the volume of the solid generated when R is revolved about the y-axis.

d. Suppose S is a solid whose base is R and whose cross sections perpendicular to R and parallel to the x-axis are semicircles. Write a single integral that gives the volume of S.

УА x = y² + 2 х у 3х — 4 4 2.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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