$6\mathrm{.}3$ Homework

$+!$ Category: Homework

Score: $0$ of $12$ points

Consider the region $R$ bounded by the line $f(x)=39-7x$ and the parabola $g(x)=29-x^2.$ To find the volume of the solid when $R$ is revolved around the $y-$axis, we should evaluate the integral:

$f{x}^{n}dx=\frac{x^{n+1}}{n+1}$

$[\frac{7x^3}{3}-\frac{x^4}{4}-\frac{10x^2}{2}{]}_2^{5}dx$

$2[\frac{7}{3}(5^3)-\frac{5^4}{4}(5^2)-(\frac{7}{3}(2^3)-\frac{2^4}{4}-5(2^2))]$

$($Note: Input the integrand in the form of $2f(x).$ Type pi to enter $)$