Problem

Find the generalized center of mass between $y=a^…

07:47

Problem 290 Hard Difficulty

Find the generalized center of mass in the sliver between $y=x^{a}$ and $y=x^{b}$ with $a > b$ . Then, use the Pappus theorem to find the volume of the solid generated when revolving around the $y$ -axis.

Answer

$(\overline{x}, \overline{y})=\left[\frac{(a+1)(b+1)}{(a+2)(b+2)}, \frac{(a+1)(b+1)}{(2 a+1)(2 b+1)}\right]$
$V=\frac{2 \pi(a-b)}{(a+2)(b+2)}$

Related Courses

Calculus 2 / BC

Calculus

Chapter 6

Applications of Integration

Section 6

Moments and Centers of Mass

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