What is the integral from 0 to pi of e^{2x} ?

The integral from 0 to pi of e^{2x} is (e^{2pi}-1)/2

Popular >

integral from 0 to pi of e^{2x}

\int_{0}^{π} e^{2 x} d x

\frac{e ^{2 π} - 1}{2}

Decimal

267.24582 \dots

Solution steps

\int_{0}^{π} e^{2 x} d x

Apply u-substitution

: \int_{0}^{2 π} e^{u} \frac{1}{2} d u

= \int_{0}^{2 π} e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2 π} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{2} [e^{u}]_{0}^{2 π}

Compute the boundaries:

e^{2 π} - 1

= \frac{1}{2} (e^{2 π} - 1)

Simplify

= \frac{e ^{2 π} - 1}{2}

\int_{- 1}^{0} x^{\frac{1}{3}} d x

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

\int_{1}^{8} (\frac{x}{2} - \frac{9}{x}) d x

\int_{0}^{2} x^{3} x^{4} + 1 d x

\int_{0}^{\infty} \frac{1}{x ^{6}} d x

What is the integral from 0 to pi of e^{2x} ?
The integral from 0 to pi of e^{2x} is (e^{2pi}-1)/2