What is the integral from 4 to 14 of 5e^{0.02x} ?

The integral from 4 to 14 of 5e^{0.02x} is 59.96068…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 4 to 14 of 5e^{0.02x}

\int_{4}^{14} 5 e^{0.02 x} d x

59.96068 \dots

Solution steps

\int_{4}^{14} 5 e^{0.02 x} d x

Take the constant out:

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

= 5 \cdot \int_{4}^{14} e^{0.02 x} d x

Apply u-substitution

: \int_{0.08}^{0.28} e^{u} \frac{1}{0.02} d u

= 5 \cdot \int_{0.08}^{0.28} e^{u} \frac{1}{0.02} d u

Take the constant out:

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

= 5 \cdot \frac{1}{0.02} \cdot \int_{0.08}^{0.28} e^{u} d u

Simplify

= 5 \cdot 50 \cdot \int_{0.08}^{0.28} e^{u} d u

Use the common integral:

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

= 5 \cdot 50 [e^{u}]_{0.08}^{0.28}

Simplify

= 250 [e^{u}]_{0.08}^{0.28}

Compute the boundaries:

0.23984 \dots

= 250 \cdot 0.23984 \dots

Simplify

= 59.96068 \dots

\int_{y}^{1} cos (x^{3}) d x

\int_{1}^{5} (- x^{2} + 3 x + 2) d x

\int_{5}^{6} 1 d x

\int_{0}^{0.1} e^{- x^{2}} d x

\int_{0}^{π} (8 e^{x} + 8 sin (x)) d x

What is the integral from 4 to 14 of 5e^{0.02x} ?
The integral from 4 to 14 of 5e^{0.02x} is 59.96068…