Integrate the function arccos(x) from 0 to 1/2

 Exercise

$\int_0^{.5}\arccos\left(x\right)dx$

 

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

$\left[\left(x\arccos\left(x\right)-\sqrt{1-x^2}\right)\right]_{0}^{0.5}$

 

Evaluate the definite integral

$0.5\arccos\left(0.5\right)-\sqrt{1- 0.5^2}-\left(0\arccos\left(0\right)-\sqrt{1- 0^2}\right)$

 

Simplify the expression

$0.5\arccos\left(0.5\right)-\sqrt{1- 0.5^2}+0\arccos\left(0\right)+1$

$0.5\arccos\left(0.5\right)-\sqrt{1- 0.5^2}+0\arccos\left(0\right)+1$

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