What is the integral from 0 to 3 of 0.2e^{-0.2x} ?

The integral from 0 to 3 of 0.2e^{-0.2x} is 0.45118…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of 0.2e^{-0.2x}

\int_{0}^{3} 0.2 e^{- 0.2 x} d x

0.45118 \dots

Solution steps

\int_{0}^{3} 0.2 e^{- 0.2 x} d x

Take the constant out:

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

= 0.2 \cdot \int_{0}^{3} e^{- 0.2 x} d x

Apply u-substitution

: \int_{0}^{- 0.6} - \frac{1}{0.2} e^{u} d u

= 0.2 \cdot \int_{0}^{- 0.6} - \frac{1}{0.2} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 0.2 (- \int_{- 0.6}^{0} - \frac{1}{0.2} e^{u} d u)

Take the constant out:

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

= 0.2 (- (- \frac{1}{0.2} \cdot \int_{- 0.6}^{0} e^{u} d u))

Simplify

= 0.2 (- (- 5 \cdot \int_{- 0.6}^{0} e^{u} d u))

Use the common integral:

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

= 0.2 (- (- 5 [e^{u}]_{- 0.6}^{0}))

Simplify

= [e^{u}]_{- 0.6}^{0}

Compute the boundaries:

0.45118 \dots

= 0.45118 \dots

\int 20 sin^{2} (x co) s^{2} x d x

\frac{d}{d x} (36 x^{\frac{1}{2}})

3 x

h \to 0 lim (\frac{h ^{2} + 2 h}{h})

\int_{0}^{1} (e^{2 x} + x^{2} + 1) d x

What is the integral from 0 to 3 of 0.2e^{-0.2x} ?
The integral from 0 to 3 of 0.2e^{-0.2x} is 0.45118…