What is the integral from 0 to pi of 2t ?

The integral from 0 to pi of 2t is pi^2

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integral from 0 to pi of 2t

\int_{0}^{π} 2 t d t

π^{2}

Decimal

9.86960 \dots

Solution steps

\int_{0}^{π} 2 t d t

Take the constant out:

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

= 2 \cdot \int_{0}^{π} t d t

Apply the Power Rule

= 2 [\frac{t ^{2}}{2}]_{0}^{π}

Compute the boundaries:

\frac{π ^{2}}{2}

= 2 \cdot \frac{π ^{2}}{2}

Simplify

= π^{2}

What is the integral from 0 to pi of 2t ?
The integral from 0 to pi of 2t is pi^2