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Definite integral

\begin{align} \int_{ 0 }^{ \pi } \sin ^2\left(x\right) \,\mathrm{d}x&= \left[ {{x}\over{2}}-{{\sin \left(2\,x\right)}\over{4}} \right]_{ 0 }^{ \pi }\\ &= {{\pi}\over{2}}-0 \\&= {{\pi}\over{2}} \\& \approx 1.570796326794897 \end{align} Help to find the primitive function

Mean value

\begin{align} \mu&=\frac{1}{b-a}\int_{a}^{b}f(x)\,\mathrm{d}x\\&=\frac{ {{\pi}\over{2}} }{ \pi }\\&= {{1}\over{2}} \\&\approx 0.5 \end{align}

Graph of the function and mean value