Question

How to get \(\int_0^4 \int_0^{\sqrt{x}} ycos(x^2)dydx\) from \(\int_0^2 \int_{y^2}^4 ycos(x^2)dxdy\)?

Answer 1

can you sketch the region
y = 0 to sqrt x
x = 0 to 4
?

Answer 2

draw the lines and parabola
y=0,
y= sqrt x
x=0
x= 4
the area is enclosed within these curves/lines