$$\ \frac{\pi\ }{4}$$

0

$$\frac{\pi\ }{2}+2$$

$$\frac{\pi\ }{2}-2$$

$$\ 8\ln8-16+e$$

$$\ln8-16$$

$$16-e$$

$$e$$

$$\ \frac{\pi\ ^2}{2}+2$$

$$\frac{\pi\ ^2}{2}$$

$$\frac{\pi\ }{2}+2$$

$$\frac{\pi\ ^2}{2}-2$$

$$\int_0^2\ \int_x^y\ \left(2y^2\ \sin\left(xy\right)\right)dxdy$$

$$\int_0^2\ \int_0^y\ \left(2y^2\ \sin\left(xy\right)\right)dxdy$$

$$\int_x^y\ \int_0^2\ \left(2y^2\ \sin\left(xy\right)\right)dxdy$$

$$\int_0^2\ \int_2^x\ \left(2y^2\ \sin\left(xy\right)\right)dxdy$$

cos4

4-sin4

4+cos2

4+sin2

$$\int_0^4\ \int_0^{\sqrt{\ 4-y^2}}\ \left(\ \frac{\ xe^{2y}}{4-y}\right)dxdy$$

$$\int_0^4\ \int_0^{4-y^2}\ \left(\ \frac{\ xe^{2y}}{4-y}\right)dxdy$$

$$\int_0^4\ \int_0^{\sqrt{\ 4-y}}\ \left(\ \frac{\ xe^{2y}}{4-y}\right)dxdy$$

$$\int_0^2\ \int_{4-x^2}^0\ \left(\ \frac{\ xe^{2y}}{4-y}\right)dxdy$$

$$\frac{e^8\ }{4}$$

$$\frac{3\ }{4}$$

$$\frac{e}{4}$$

$$\frac{e^8-1\ }{4}$$

$$\int_0^1\ \int_0^{\sqrt{1-r^2\ }}\ r^3drd\theta\$$

$$\int_0^{\frac{\pi}{2}}\ \int_0^{1\ }\ r^3drd\theta\$$

$$\int_0^{\pi\ }\ \int_0^{1\ }\ r^3drd\theta\$$

$$\int_0^{\frac{\pi}{2}}\ \int_0^{1\ }\ r^2drd\theta\$$

15

20

$$\frac{128}{15}$$

125