Hello, can someone help me. thank you sir.

Question

Evaluate the following iterated intergal by changing the order of integration (give answer accurate to four decimal places)

∫₀¹ ∫_2y² 4cos(x²)dxdy

Answer 1

∫₀¹∫_2y²4cos(x²)dxdy = ∫₀²∫₀^x/24cosx²dydx = ∫₀²4cos(x²)y₀^x/2dx = ∫₀²2xcos(x²)dx = sin(x²)₀² = sin4