What is the integral from 1 to sqrt(3 of) 4/(x^2+1) ?

The integral from 1 to sqrt(3 of) 4/(x^2+1) is pi/3

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integral from 1 to sqrt(3 of) 4/(x^2+1)

\int_{1}^{3} \frac{4}{x ^{2} + 1} d x

\frac{π}{3}

Decimal

1.04719 \dots

Solution steps

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

Use the common integral:

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

= 4 [arctan (x)]_{1}^{3}

Compute the boundaries:

\frac{π}{12}

= 4 \cdot \frac{π}{12}

Simplify

= \frac{π}{3}

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What is the integral from 1 to sqrt(3 of) 4/(x^2+1) ?
The integral from 1 to sqrt(3 of) 4/(x^2+1) is pi/3