What is the solution to ∫x^2(x+1)^1/2 for x=0 x=3?

[Jimbo57]

Homework Statement

Integrate x^2(x+1)^1/2 for x=0 x=3

Homework Equations

The Attempt at a Solution

I start with substitution u=x+1
and du=dx

I have no clue where to go from here. How do I take care of that x^2?

This looks like it would be simple but it's giving me a hell of a time.

Jim

 

[danny_manny]

Try integration by parts.

 

[SammyS]

Homework Statement

Integrate x^2(x+1)^1/2 for x=0 x=3

Homework Equations

The Attempt at a Solution

I start with substitution u=x+1
and du=dx

I have no clue where to go from here. How do I take care of that x^2?

This looks like it would be simple but it's giving me a hell of a time.

Jim

That substitution, u=x+1, should work fine, and allow you to complete the integration.

What do you get for the integrand when you use that substitution?

 

[Jimbo57]

Looking through my textbook I realized that we already solved this one as an indefinite integral... kind of embarrassing.

Dealing with the x^2 was the hardest, but the integrand is:

u=x+1
du=dx
x^2=(u-1)^2 <---- Much easier looking at it now.

∫(u-1)^2u^1/2du

Thanks for the help as always!