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

The integral from-1 to 1 of arccos(x) is pi

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integral from-1 to 1 of arccos(x)

\int_{- 1}^{1} arccos (x) d x

π

Decimal

3.14159 \dots

Solution steps

\int_{- 1}^{1} arccos (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

π

= π

\int_{0}^{1} 3 x^{2} + 1 d x

\int_{0}^{4} \frac{x}{16 - x ^{2}} d x

\int_{5}^{11} \frac{1}{x ^{2}} d x

\int_{0}^{4} e^{3 x} d x

\int_{- 3}^{0} x d x

What is the integral from-1 to 1 of arccos(x) ?
The integral from-1 to 1 of arccos(x) is pi