Relation with counting volume of a solid revolution

[b00tofuu]

Homework Statement

let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2)

The Attempt at a Solution

i have a feeling that it has a relation with counting volume of a solid revolution.but i don't know how to answer it...

 

[tiny-tim]

Hi b00tofuu!

(try using the X² tag just above the Reply box )

let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2)

Do you mean ∫₀² 1/(x³ + x⁵)² dx ?

If so, factor it, and then use partial fractions.

 

[b00tofuu]

no, it's not what i meant...
its the squared of the inverse function of (x^3+x^5).
a.the question first asked about the volume of solid revolution of a function y=f(x) bounded by y=b, and the y axis. the function crossed (0,0),(a,b) where a>0. i'vc got the answer
int(phi(f(y)^-1)^2, y = 0 .. b) by the disk method.
then the second point of the question is where i have the problem
b. let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2)

i think it's related to each other... but dunno...

 

[tiny-tim]

(please use the X² tag just above the Reply box )

ah, you meant ∫₀² (f^-1(x))² dx.

ok, put y = x³ + x⁵, then that's …

∫y² dx, so substitute (something)dy for dx, change the limits, and integrate over y.