What is the integral from 1 to 5 of 2e^{2x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 5 of 2e^{2x}

\int_{1}^{5} 2 e^{2 x} d x

e^{10} - e^{2}

Decimal Notation

22019.07673 \dots

Solution steps

\int_{1}^{5} 2 e^{2 x} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{5} e^{2 x} d x

Apply u-substitution

: \int_{2}^{10} e^{u} \frac{1}{2} d u

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

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

Use the common integral:

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

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

Simplify

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

= [e^{u}]_{2}^{10}

Compute the boundaries:

e^{10} - e^{2}

= e^{10} - e^{2}

x \to - 0.001 lim (4 x^{2} + 7)

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 18 y - x)

\frac{\partial}{\partial y} (9 x sin (y - z))

\int_{- 4}^{- 1} x^{4} d x

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