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

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

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

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

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

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

Take the constant out:

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

= 2 \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)

= 2 [arctan (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 2 \cdot \frac{π}{4}

Simplify

= \frac{π}{2}

\frac{d}{d x} (x^{4} + y^{4} + z^{4})

\frac{d}{d x} (sin (7 x^{2}))

x \frac{d y}{d x} = 7 x e^{x} - y + 9 x^{2}

x \to 1 lim (\frac{2}{x ^{2} - 7 x + 6})

f (x) = x^{3} cos (x)

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