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

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

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

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

arctan (2)

Decimal

1.10714 \dots

Solution steps

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

Use the common integral:

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

= [arctan (y)]_{0}^{2}

Compute the boundaries:

arctan (2)

= arctan (2)

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\int_{0}^{2} \frac{1}{3 x + 5} d x

\int_{1}^{70} \frac{70}{69 x ^{2}} d x

\int_{- 1}^{3} x^{4} d x

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