Evaluate the integral by reversing the order of integration

Question

1 1

∫ ∫ sin(x^2) dxdy

0 y

? ?

= ∫ ∫ sin(x^2) dydx

? ?

Answer 1

1 1

∫ ∫ sin(x²) dxdy

0 y

1 x

= ∫ ∫ sin(x²) dydx

0 0

1

= ∫ xsin(x²)/2 dx = -cos(x²)/2 |₀¹ = (-cos(1)+1)/2

0