Commutative integral order ∫ (4,0) DX ∫ (x, 2x ^ 0.5) f (x, y) dy

Commutative integral order ∫ (4,0) DX ∫ (x, 2x ^ 0.5) f (x, y) dy

The range of X is 0 to 4,
And the range of Y is x to 2 √ X
Draw the integral range,
So instead of integrating x first,
The range of X is 0.25y to y,
And the range of Y is 0 to 4,
So the exchange integral order is obtained
Original integral
=∫(4.0) dy ∫(y,0.25y²) f(x,y)dx