Question

Find the volume of the solid that results when the region enclosed by the curves is revolved about the x-axis.

Answer 1

A

Explanation:

`volume=\pi \int\limits^0_(-1) {[(-x^2+7)^2-({x+5)^2}] } \, dx \\\\=\pi\int\limits^0_(-1)[( {x^4-14x^2+49})-(x^2+10x+25)] \, dx \\=\pi \int\limits^0_(-1) {[x^4-15x^2+10x+24] } \, dx =\pi [((x^5)/(5) -15(x^3)/(3)+10 (x^2)/(2) +24x)]| x: ~-1 \rightarrow 0\\=\pi [(1)/(5)(0-(-1))-5(0-(-1))+5(0-(-1))+24(0-(-1)]\\=\pi [(1)/(5)-5+5+24]\\=24(1)/(5) \pi\\=(121 \pi)/(5)\\\approx ~76.02 ~units~cubed`