What is the integral from 0 to 1 of 2arccos(x) ?

The integral from 0 to 1 of 2arccos(x) is 2

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integral from 0 to 1 of 2arccos(x)

\int_{0}^{1} 2 arccos (x) d x

2

Solution steps

\int_{0}^{1} 2 arccos (x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{1} arccos (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

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What is the integral from 0 to 1 of 2arccos(x) ?
The integral from 0 to 1 of 2arccos(x) is 2