Yes you should be getting the same answers. Here I'll show you a simpler example. Consider the integral

In your triangle put the hypotenuse equal to 1. The leg that is across the angle should be x so that

Now using Pythagoras theorem the other leg is

Now you can write the integral like this

You have to express

in terms of

We have

and we differentiate both sides to get

Now we substitute dx in the integral to get

What you do next is change the limits of integration. The limits are x=0 and x=1 but we are integrating with respect to

You use

and you need to solve the two equations.

and

You have to work in radians. The reason for that is because radians have a unit of length which is the same unit for x and y.

Now your integral becomes