Integrate the function sin(x)^2 from pi to x^(1/2)

 Exercise

$\int_{\pi}^{\sqrt{x}}\left(\sin\left(x\right)^2\right)dx$

 

Apply the formula: $\int\sin\left(\theta \right)^2dx$$=\frac{1}{2}\theta -\frac{1}{4}\sin\left(2\theta \right)+C$

$\left[\left(\frac{1}{2}x-\frac{1}{4}\sin\left(2x\right)\right)\right]_{\pi }^{\sqrt{x}}$

 

Evaluate the definite integral

$\frac{1}{2}\sqrt{x}-\frac{1}{4}\sin\left(2\sqrt{x}\right)-\left(\pi \left(\frac{1}{2}\right)-\frac{1}{4}\sin\left(2\pi \right)\right)$

 

Simplify the expression

$\frac{1}{2}\sqrt{x}-\frac{1}{4}\sin\left(2\sqrt{x}\right)-\frac{\pi }{2}+\frac{1}{4}\sin\left(2\pi \right)$

$\frac{1}{2}\sqrt{x}-\frac{1}{4}\sin\left(2\sqrt{x}\right)-\frac{\pi }{2}+\frac{1}{4}\sin\left(2\pi \right)$

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