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

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

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

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

\frac{π}{4}

Decimal

0.78539 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

\frac{π}{4}

= \frac{π}{4}

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\int_{0}^{2} 8 x^{2} d x

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