What is the integral from 0 to 5 of 4-10e^{-0.2x} ?

The integral from 0 to 5 of 4-10e^{-0.2x} is (50)/e-30

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 5 of 4-10e^{-0.2x}

\int_{0}^{5} 4 - 10 e^{- 0.2 x} d x

\frac{50}{e} - 30

Decimal

- 11.60602 \dots

Solution steps

\int_{0}^{5} 4 - 10 e^{- 0.2 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} 4 d x - \int_{0}^{5} 10 e^{- 0.2 x} d x

\int_{0}^{5} 4 d x = 20

\int_{0}^{5} 10 e^{- 0.2 x} d x = 50 (1 - \frac{1}{e})

= 20 - 50 (1 - \frac{1}{e})

Simplify

20 - 50 (1 - \frac{1}{e}) : \frac{50}{e} - 30

= \frac{50}{e} - 30

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (2 x) d x

\int_{0}^{10} 2000 - 12 x^{2} d x

\int_{2}^{3} 5^{3 x} d x

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

\int_{1}^{4} y d y

What is the integral from 0 to 5 of 4-10e^{-0.2x} ?
The integral from 0 to 5 of 4-10e^{-0.2x} is (50)/e-30