Integrate 0 to a: xsqrt(x^2+a^2)dx

[Xetman]

Homework Statement

http://i50.tinypic.com/zxw6qr.png

a>0

a
∫ x√(x^2+a^2)dx (a>0)
02. The attempt at a solution

u=x^2+a^2
du=2xdx

I looked it up online and I saw you needed to use trig.
How do you use trig for this problem?

Note: I have not learned integration by parts, just u-sub.

 

[Dick]

Homework Statement

http://i50.tinypic.com/zxw6qr.png

a>0

a
∫ x√(x^2+a^2)dx (a>0)
0


2. The attempt at a solution

u=x^2+a^2
du=2xdx

I looked it up online and I saw you needed to use trig.
How do you use trig for this problem?

Note: I have not learned integration by parts, just u-sub.

You don't need trig for this problem. Just continue with your substitution.

 

[Mentallic]

Homework Statement

http://i50.tinypic.com/zxw6qr.png

a>0

a
∫ x√(x^2+a^2)dx (a>0)
0


2. The attempt at a solution

u=x^2+a^2
du=2xdx

I looked it up online and I saw you needed to use trig.
How do you use trig for this problem?

Note: I have not learned integration by parts, just u-sub.

As Dick said, you can just continue with your u-sub and you'll find the problem can be solved relatively easily. Now, you could solve it by using trig substitution but it does become more difficult, and you'd need to do 2 substitutions as well.

But if you want to try it out anyway, start by letting $x=a\cdot \tan(\theta)$