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## Homework Statement

Integrate √(x

^{2}(x+3)) from -3 to 0.

0

∫√(x

^{2}(x+3)) dx

-3

**2. The attempt at a solution**

Here is what I did:

√(x

^{2}(x+3))

= x√(x+3)

Let u=x+3, du=dx, x=u-3

Insert the bounds and change the bounds to: 0 to 3.

x√(x+3)=

(u-3)√(u)

= u

^{3/2}-3u

^{1/2}

Thus we have:

3

∫(u

^{3/2}-3u

^{1/2}) du

0

Finally:

(2u

^{5/2})/5-(2u

^{3/2}) from 0 to 3.

Thus I get: -4.15.

However the correct answer is positive 4.15.

I know the answer should be positive but what I don't understand is why I'm getting a negative answer. Please help.

Thanks in advance.