calculus II
posted by saud on .
Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=x^8/9 about the xaxis over the interval [1,2].

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=(2)/(x+1) about the xaxis over the interval [0,4].

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=e^x about the xaxis over the interval [0,2].

is that f(x) = x^(8/9) or f(x) = (x^8)/9
is will assume the latter.
Volume = π[integral) (x^16)/81 dx from 1 to 2
= π[x^17)/(17(81)) ] from 1 to 2
= π(2^17/(17(81))  1/(17(81))
= .... 
second one:
volume = π[integral] 4/(x+1)^2 from 0 to 2
= π((4/(x+1)) from 0 to 2
= π(4/3  (4/1)
= ....
third one:
you try it, the integral of (e^x)^2 is (1/2)e^(2x)