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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 4 [arctan (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 4 \cdot \frac{π}{4}

Simplify

= π

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