What is the integral from 0 to c of 10e^{2x} ?

The integral from 0 to c of 10e^{2x} is 5(e^{2c}-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to c of 10e^{2x}

\int_{0}^{c} 10 e^{2 x} d x

5 (e^{2 c} - 1)

Solution steps

\int_{0}^{c} 10 e^{2 x} d x

Take the constant out:

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

= 10 \cdot \int_{0}^{c} e^{2 x} d x

Apply u-substitution

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

= 10 \cdot \int_{0}^{2 c} 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

= 10 \cdot \frac{1}{2} \cdot \int_{0}^{2 c} e^{u} d u

Use the common integral:

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

= 10 \cdot \frac{1}{2} [e^{u}]_{0}^{2 c}

Simplify

10 \cdot \frac{1}{2} [e^{u}]_{0}^{2 c} : 5 [e^{u}]_{0}^{2 c}

= 5 [e^{u}]_{0}^{2 c}

Compute the boundaries:

e^{2 c} - 1

= 5 (e^{2 c} - 1)

\int (\frac{3}{x ^{3}}) d x

\frac{d}{d t} (e^{i t})

\frac{d x}{d t} = sin (2 π (t + 3))

1

What is the integral from 0 to c of 10e^{2x} ?
The integral from 0 to c of 10e^{2x} is 5(e^{2c}-1)