Expand the integral $\int_{\frac{\pi }{2}}^{\pi }\left(\cos\left(x\right)+3\sin\left(x\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $\int_{\frac{\pi }{2}}^{\pi }\cos\left(x\right)dx$ results in: $-1$
The integral $\int_{\frac{\pi }{2}}^{\pi }3\sin\left(x\right)dx$ results in: $3$
Gather the results of all integrals
Subtract the values $3$ and $-1$
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