What is the integral from 0 to pi/4 of 1/(x^2+1) ?

The integral from 0 to pi/4 of 1/(x^2+1) is arctan(pi/4)

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integral from 0 to pi/4 of 1/(x^2+1)

\int_{0}^{\frac{π}{4}} \frac{1}{x ^{2} + 1} d x

arctan (\frac{π}{4})

Decimal

0.66577 \dots

Solution steps

\int_{0}^{\frac{π}{4}} \frac{1}{x ^{2} + 1} d x

Use the common integral:

\int \frac{1}{x ^{2} + 1} d x = arctan (x)

= [arctan (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

arctan (\frac{π}{4})

= arctan (\frac{π}{4})

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What is the integral from 0 to pi/4 of 1/(x^2+1) ?
The integral from 0 to pi/4 of 1/(x^2+1) is arctan(pi/4)