Could someone explain me the following integral step by step using trigonometric sustitution? Indefinite integral

Question

anonymous · Answer

$$\int\limits_{a}^{b}\sqrt{9-x^{2}}$$

anonymous · Answer

I tried it by myself and wolfram and I are different in just 1 number, he's dividing a part by 2 and I'm not, so help would be appreciated, I can take a picture of my procedure.

chaise · Answer

Recall that when you integrate you divide by the derivative of the inner function, in this case, the derivative of the inner function is x^2, whose derivative is 2x. 

Wolfram alpha might also have an extra x in there too, that you are missing.

anonymous · Answer

The deal is that I was asked to do this using trigonometric sustitution for my homework, and since this is the first time I integrate using this method I need some explanation heh.

chaise · Answer

Well, you need to make this substution:

$$\sqrt{a^2-x^2} --> asin(x)$$

In this case, your a will be 3.

chaise · Answer

Try watching this video :) https://www.youtube.com/watch?v=3lC5AuCFK4c

anonymous · Answer

I got it right already, thank you!