To answer your question, assume you take a small slice of the ellipse in the second quadrant, where . This is the 'width' of the slice from the y-axis. The height of the slice is . Since a and b are constants, you would treat them just as if they were 2 and 3.
So take the definite integral of (from y=0 to y=b defines the entire part of the ellipse in the 2nd quadrant). You may want to review trigonometric substitution to get this integral!