Int((2−cos(x+y)dxdy) when D is the bounded region enclosed by the lines x+y = π ,x=0 and y=0.

its a double integral problem

∫∫D (2 - cos(x+y)) dA
= ∫(x = 0 to π) ∫(y = 0 to π-x) (2 - cos(x+y)) dy dx
= ∫(x = 0 to π) (2y - sin(x+y)) {for y = 0 to π-x} dx
= ∫(x = 0 to π) [(2(π-x) - sin(x+ π-x)) - (-sin x)] dx
= ∫(x = 0 to π) (2π - 2x + sin x) dx
= (2πx - x^2 - cos x) {for x = 0 to π}
= π^2 + 2.

I hope this helps!