# calculus II

posted by .

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=x^8/9 about the x-axis over the interval [1,2].

• calculus II -

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

• calculus II -

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

• calculus II -

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))
= ....

• calculus II -

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)

## Similar Questions

1. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^(3) and x= y^(1/3) about the y-axis over the interval [0,1].
2. ### Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
3. ### calculus

Find the volume of the solid obtained by rotating the region under the graph f(x) = x2 - 3x about the x-axis over the interval [0, 3].
4. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 …
5. ### Calculus

Find the volume of the solid obtained by rotating the region under the graph of the function f(x) = (2)/(x+1) about the x-axis over the interval [0,3]
6. ### Math: Calc 2

Find the volume of the solid obtained by rotating the region under the graph of the function f(x) = x^(13/12) about the x-axis over the interval [1,3]. Thanks!
7. ### MATH HELP

Find the volume of the solid obtained by rotating the region underneath the graph of f(x) = (x)/sqrt(x^3+1) about the y-axis over the interval (1, 10)
8. ### Calculus 1

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=2x+1 about the x-axis over the interval [0,1]. I have no clue how to start this..... :(
9. ### Calculus

Find the volume of the solid obtained by rotating the region under the graph of f(x)= 9-x^2 for 0<= x<=3 about the vertical axis x= -2. My answer: 81 pi/2
10. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^{5} and x=5sqrty about the y-axis over the interval [0,1].

More Similar Questions