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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

\frac{π}{4}

= 4 \cdot \frac{π}{4}

Simplify

= π

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

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