Essential Calculus Early Transcendentals

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.

$$y=x^{2}, x^{2}+y^{2}=1, y \geqslant 0$$

(a) About the $x$ -axis (b) About the $y$ -axis

Essential Calculus Early Transcendentals

A CAT scan produces equally spaced cross-sectional views

of a human organ that provide information about the organ

otherwise obtained only by surgery. Suppose that a CAT

scan of a human liver shows cross-scctions spaced 1.5 $\mathrm{cm}$

apart. The liver is 15 $\mathrm{cm}$ long and the cross-sectional areas,

in square centimeters, are $0,18,58,79,94,106,117,128,$

$63,39,$ and $0 .$ Use the Midpoint Rulc to estimate the volume of the liver.