Nanya dong Integral Lipat Dua

[tex]\displaystyle \int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin x\cos y+\cos x\sin y\,dxdy\\\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=\int\limits^{\frac12\pi}_0\sin x\sin y-\cos x\cos y|^{\frac12\pi}_0\,dx\\\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=\int\limits^{\frac12\pi}_0\sin x(\sin\frac12\pi-\sin0)-\cos x(\cos\frac12\pi-\cos0)\,dx[/tex]
[tex]\displaystyle \int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=\int\limits^{\frac12\pi}_0\sin x(1-0)-\cos x(0-1)\,dx\\\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=\int\limits^{\frac12\pi}_0\sin x+\cos x\,dx\\\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=-\cos x+\sin x|^{\frac12\pi}_0\\\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=-(\cos\frac12\pi-\cos0)+(\sin\frac12\pi-\sin0)[/tex]
[tex]\displaystyle \int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=-(0-1)+(1-0)\\\boxed{\boxed{\int\limits^{\frac12\pi}_0\int\limits^{\frac12\pi}_0\sin(x+y)\,dxdy=2}}[/tex]