Mistake in provided solutions?

[unscientific]

Homework Statement

The problem is attached in the picture.

The Attempt at a Solution

If you refer to line 2 of the working, they substituted x with 'b' instead of y with 'b' since the first integral is with respect to y.

Is this a mistake or is there something more?

 

[clamtrox]

Looks to me like they're substituting x=a and x=0 on line 2, just like you'd expect.

 

[HallsofIvy]

The first integral is NOT with respect to y, it is with respect to x.

 

[unscientific]

I got a different answer when I integrated with respect to y first... I am missing the additional sqrt(b) term..

 

[clamtrox]

Then you made a mistake somewhere :-)

 

[unscientific]

Then you made a mistake somewhere :-)

You are right, I saw my mistake.. Thanks btw!