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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{- 1}^{1} \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

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

Compute the boundaries:

\frac{π}{2}

= 2 \cdot \frac{π}{2}

Simplify

= π

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