# Double integral help

$$\int _0 ^{\pi/3} \int _0 ^{\pi/4} x cos(x+y) dy dx$$
$$\int _0 ^{\pi/3} xsin(x+\frac{\pi}{4}) dx$$
using u-sub, u=x, dv=sin(x+pi/4)

$$-xcos\left(x+\frac{\pi}{4}\right)+ sin\left(x+\frac{\pi}{4}\right)-sin\left(\frac{\pi}{4}\left) |_0^{\pi/3}$$

$$-\frac{\pi}{3}cos\left(\frac{\pi}{3}+\frac{\pi}{4}\right)+ sin\left(\frac{\pi}{3}+\frac{\pi}{4}\right)-sin\left(\frac{\pi}{4}\right)$$

i dont know where I made the mistake

Last edited:

Don't forgot the lower limit in the first integration: $\sin(x+\pi/4)-\sin(x)$