Integrate the function 10arccos(x) from 0 to 1/2

 Exercise

$\int_0^{\frac{1}{2}}10\arccos\left(x\right)dx$

 

The integral of a constant times a function is equal to the constant multiplied by the integral of the function

$10\int_{0}^{\frac{1}{2}}\arccos\left(x\right)dx$

 

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

$10\left[\left(x\arccos\left(x\right)-\sqrt{1-x^2}\right)\right]_{0}^{\frac{1}{2}}$

 

Evaluate the definite integral

$10\left(\frac{1}{2}\arccos\left(\frac{1}{2}\right)-\sqrt{1- \left(\frac{1}{2}\right)^2}-\left(0\arccos\left(0\right)-\sqrt{1- 0^2}\right)\right)$

$10\left(\frac{1}{2}\arccos\left(\frac{1}{2}\right)-\sqrt{1- \left(\frac{1}{2}\right)^2}-\left(0\arccos\left(0\right)-\sqrt{1- 0^2}\right)\right)$

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