Evaluate the definite integral: (X+1)^2 from x=0 to x=-8
I tried using F(b)-F(a) but it didn't work

Question

Evaluate the definite integral: (X+1)^2 from x=0 to x=-8 
I tried using F(b)-F(a) but it didn't work

anonymous · Answer

I think an easy way to see it is by u substitution. Integrate then evaluate.

anonymous · Answer

how do you do that?

anonymous · Answer

So if you set u=x+1 then du=dx so your integral: u^(2)du. Integrate that like normal, then when you're done get the answer back in terms of x and use your limits. Or you can change your limits using u=x+1.

anonymous · Answer

ahhh kk I'll try that

anonymous · Answer

totally worked thanks man!

anonymous · Answer

$$\int (1+x)^2 dx =\frac{1}{3} (x+1)^3=F(x)\

F(-8)-F(0)=-\frac{344}{3}
$$

anonymous · Answer

No problem.

anonymous · Answer

can I use that for integrals that have like x(x^2+5)^5?

anonymous · Answer

its not a definite one but

anonymous · Answer

nvm we didn't learn those types yet

anonymous · Answer

getting ahead of myself

turingtest · Answer

you can use u-substitution for the last integral you posted
u=x^2+5
if you still don't understand pleas post this as a separate question
thanks :)

anonymous · Answer

Yes, and when you take the derivative to get du you'll find that things will cancel.