1. Evaluating an Integral

Assuming ∫ = the integral from (0-3)

I am having trouble deciding what to sub in as u in this integration problem:

∫ x(sqrt(x+1)) dx

Thanks.

2. Re: Evaluating an Integral

Let $\displaystyle u = x+1$, $\displaystyle du = dx$

The integral can then be rewritten as:

$\displaystyle \int_{0}^{3} (u-1)(\sqrt{u})du$

I'm sure you can take it from here.

3. Re: Evaluating an Integral

Originally Posted by Walshy
Assuming ∫ = the integral from (0-3)

I am having trouble deciding what to sub in as u in this integration problem:

∫ x(sqrt(x+1)) dx

The integral $\displaystyle \int_0^3 {x\sqrt {x + 1} dx}$ becomes $\displaystyle \int_1^4 {(u - 1)\sqrt u du}$.

Do you see how?

4. Re: Evaluating an Integral

Yes, I see. Thanks for the help guys.

5. Re: Evaluating an Integral

Let $\displaystyle u = x+1$, $\displaystyle du = dx$

The integral can then be rewritten as:

$\displaystyle \color{red}\int_{0}^{3} (u-1)(\sqrt{u})du$
The limits of integration are not correct.

6. Re: Evaluating an Integral

Given this, I should clarify that my bounds were regards to X, so when you integrate, you should back substitute U so you are in respect to X before evaluation of the bounds.

You can change the bounds so that they are with respect to U and integrate.

Or, you can leave the bounds with regard to X, integrate with respect to U and then back substitute so that you end up with the original function (f(x), not not f'(x)) with respect to X.

Same result.