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

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

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

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

\frac{π}{4}

Decimal

0.78539 \dots

Solution steps

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

Use the common integral:

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

= [arctan (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= \frac{π}{4}

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