Find the volume of the solid formed by revolving the region bounded by y =4 - x^2 and y=0 about the x-axis.?

Question

I got .... 1296p/5

Answer 1

Huh? Is this from the English language?

Answer 2

circle radius = r(x) = 4-x²
circle area = pi * r² = pi*(4-x²)²
volume per dx = area*dx = dv
volume = ∫dv =
2*pi*∫{from 0 to 2} (4-x²)²dx =
2*pi*∫{..}(16-8x²+x^4)dx=
2*pi(16x-8x^3/3+x^5/5)|2,0=
2*pi(16*2-(2^3)*8/3+(2^5)/5)=
2*pi(32-64/3+32/5)=
64pi*(1-2/3+1/5)=
64pi(15-10+3)/15=
64pi*8/15=
512pi/15