What is the integral from 0 to 60 of 100e^{-0.01x} ?

The integral from 0 to 60 of 100e^{-0.01x} is 4511.88363…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 60 of 100e^{-0.01x}

\int_{0}^{60} 100 e^{- 0.01 x} d x

4511.88363 \dots

Solution steps

\int_{0}^{60} 100 e^{- 0.01 x} d x

Take the constant out:

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

= 100 \cdot \int_{0}^{60} e^{- 0.01 x} d x

Apply u-substitution

: \int_{0}^{- 0.6} - \frac{1}{0.01} e^{u} d u

= 100 \cdot \int_{0}^{- 0.6} - \frac{1}{0.01} e^{u} d u

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

= 100 (- \int_{- 0.6}^{0} - \frac{1}{0.01} e^{u} d u)

Take the constant out:

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

= 100 (- (- \frac{1}{0.01} \cdot \int_{- 0.6}^{0} e^{u} d u))

Simplify

= 100 (- (- 100 \cdot \int_{- 0.6}^{0} e^{u} d u))

Use the common integral:

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

= 100 (- (- 100 [e^{u}]_{- 0.6}^{0}))

Simplify

= 10000 [e^{u}]_{- 0.6}^{0}

Compute the boundaries:

0.45118 \dots

= 10000 \cdot 0.45118 \dots

Simplify

= 4511.88363 \dots

y = x e^{9 x}

\frac{1}{3} (x^{2} - 2)^{\frac{3}{2}}

\int \frac{( x ^{2} - x + 36 )}{x ^{3} + 6 x} d x

y = 2 sin (x), (\frac{π}{6}, 1)

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

What is the integral from 0 to 60 of 100e^{-0.01x} ?
The integral from 0 to 60 of 100e^{-0.01x} is 4511.88363…