What is the integral from 0 to 1 of 6/(t^2+1) ?

The integral from 0 to 1 of 6/(t^2+1) is (3pi)/2

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integral from 0 to 1 of 6/(t^2+1)

\int_{0}^{1} \frac{6}{t ^{2} + 1} d t

\frac{3 π}{2}

Decimal

4.71238 \dots

Solution steps

\int_{0}^{1} \frac{6}{t ^{2} + 1} d t

Take the constant out:

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

= 6 \cdot \int_{0}^{1} \frac{1}{t ^{2} + 1} d t

Use the common integral:

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

= 6 [arctan (t)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 6 \cdot \frac{π}{4}

Simplify

= \frac{3 π}{2}

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What is the integral from 0 to 1 of 6/(t^2+1) ?
The integral from 0 to 1 of 6/(t^2+1) is (3pi)/2