Consider the shaded triangular region P shown in the figure.

Consider the shaded triangular region P shown in the figure. What is ∬_{_P} xy dxdy ?

I = ∬ xy .dxdy

The limit of y is from 0 to

and limit of x from 0 to 2.

=		x		1 -	x		²	dx
		2			2

=	1		x(x² + 4 - 4x).dx
	8

=	1		(x³ + 4x - 4x²).dx
	8