Question

Find the volume of the solid obtained by rotating the region underneath the graph of f(x)=(x)/(sqrt(x^3+5))， about the y-axis over the interval [1, 10].

Answer 1

which method do you want to use to do this?

Answer 2

using the shell method you would integrate from a to be over 2 pi (shell radius) (shell height) dx.

Answer 3

\[\int\limits_{1}^{10}2\pi*(x)(\frac{ x }{ x^3 }+5)\]

Answer 4

pull the 2 pi out front and distribute the x. then simplify

Answer 5

i can do it from here

Answer 6

woo okay. good luck!

Answer 7

i integrated it and got 1570

Answer 8

\[\int\limits\limits_{1}^{10}2\pi*(x)\frac{ x }{ \sqrt{x^3+5} }dx\]

Answer 9

yeah?

Answer 10

\[2\pi \int\limits_{1}^{10}\frac{ x^2 }{(x^3+5)^{1/2} }dx\]

Answer 11

this looks nasty so lets look for a substitution. let u = x^3+5... du = 3x^2 dx...1/3 du = x^2 dx

Answer 12

your answer was not correct.. why i am still explaining.

Answer 13

your answer is only of by 1400+

Answer 14

answer is 122, i see what i did wrong.