Answer
$\frac{1}{2}sin(1)$
Work Step by Step
Given: $\int_{0}^{1}\int_{x}^{1}cos(y^{2})dydx$
Integrate by switching order of integration.
Since, $x=1$ and $x=0$ , putting this into $ y=x$ we get $y=0, y=1$ ,$x=y$, $x=0$
$=\int_{0}^{1}\int_{0}^{y}cos(y^{2})dxdy$
$=\int_{0}^{1}xcos(y^{2})|_{0}^{y}dy$
$=\int_{0}^{1}[ycos(y^{2})-0]|dy$
$=\frac{1}{2}sin(y^{2})|_{0}^{1}$
$=\frac{1}{2}sin(1)$
