Double Integral Help: Solving for e^sin(x) over D

[asdf12312]

double integral help??

Homework Statement

Evaluate the double integral

| | e^sin(x) dA
over the region
D = {(x,y) | 0 ≤ x ≤ π/2, 0 ≤ y ≤ cosx} .

Homework Equations

The Attempt at a Solution

how would i do this? i know that dA = dy(dx) so the integral would be
|(0 ≤ x ≤ π/2) |(0 ≤ y ≤ cosx) (e^sin(x) dy) dx

would i have to switch the integration? so it would be dx(dy) instead? or could i just integrate it with respect to dy and say it is y*e^sin(x)?

 

[hsetennis]

Order of iteration in such a double integral does not matter.

Edit: you're in the right direction.

 

[asdf12312]

OK, then i guess the rest is easy. i did get y*e^sin(x) when i integrated with respect to dy and my final answer was e¹ - e⁰ = 1.718