## Calculus: Early Transcendentals 8th Edition

$\frac{1}{2}sin(1)$
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 $y=0, y=1$ ,$x=y$, $x=0$ $=\int_{0}^{1}\int_{0}^{y}cos(y^{2})dxdy$ $=\int_{0}^{1}xcos(y^{2})|_{0}^{y}dy$ $=\int_{0}^{1}[ycos(y^{2})-0]|dy$ $=\frac{1}{2}sin(y^{2})|_{0}^{1}$ $=\frac{1}{2}sin(1)$