What is the integral from 0 to 0.5 of 5arccos(x) ?

The integral from 0 to 0.5 of 5arccos(x) is 3.28786…

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integral from 0 to 0.5 of 5arccos(x)

\int_{0}^{0.5} 5 arccos (x) d x

3.28786 \dots

Solution steps

\int_{0}^{0.5} 5 arccos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{0.5} arccos (x) d x

Apply Integration By Parts

= 5 [x arccos (x) - \int - \frac{x}{1 - x ^{2}} d x]_{0}^{0.5}

\int - \frac{x}{1 - x ^{2}} d x = 1 - x^{2}

= 5 [x arccos (x) - 1 - x^{2}]_{0}^{0.5}

Compute the boundaries:

0.65757 \dots

= 5 \cdot 0.65757 \dots

Simplify

= 3.28786 \dots

What is the integral from 0 to 0.5 of 5arccos(x) ?
The integral from 0 to 0.5 of 5arccos(x) is 3.28786…