What is the integral from 1 to 4 of 5e^{sqrt(x)} ?

The integral from 1 to 4 of 5e^{sqrt(x)} is 10e^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 4 of 5e^{sqrt(x)}

\int_{1}^{4} 5 e^{x} d x

10 e^{2}

Decimal Notation

73.89056 \dots

Solution steps

\int_{1}^{4} 5 e^{x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{4} e^{x} d x

Apply u-substitution

: \int_{1}^{2} e^{u} \cdot 2 u d u

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

Take the constant out:

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

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

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{1}^{2}

= 5 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

= 5 \cdot 2 [e^{u} u - e^{u}]_{1}^{2}

Simplify

= 10 [e^{u} u - e^{u}]_{1}^{2}

Compute the boundaries:

e^{2}

= 10 e^{2}

y^{^{''}} + 81 y = 5 tan (9 x)

\int \frac{x ^{2}}{2 x ^{2} - 9} d x

x \to - 1 lim (7 x + 2)

\int_{- 6}^{8} \frac{x}{2} + 8 d x

\int x^{5} 5 + x^{6} d x

What is the integral from 1 to 4 of 5e^{sqrt(x)} ?
The integral from 1 to 4 of 5e^{sqrt(x)} is 10e^2