What is the integral from 0 to 0.8 of e^{-x} ?

The integral from 0 to 0.8 of e^{-x} is 0.55067…

Popular >

integral from 0 to 0.8 of e^{-x}

\int_{0}^{0.8} e^{- x} d x

0.55067 \dots

Solution steps

\int_{0}^{0.8} e^{- x} d x

Apply u-substitution

: \int_{0}^{- 0.8} - e^{u} d u

= \int_{0}^{- 0.8} - e^{u} d u

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

= - \int_{- 0.8}^{0} - e^{u} d u

Take the constant out:

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

= - (- \int_{- 0.8}^{0} e^{u} d u)

Use the common integral:

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

= - (- [e^{u}]_{- 0.8}^{0})

Simplify

= [e^{u}]_{- 0.8}^{0}

Compute the boundaries:

0.55067 \dots

= 0.55067 \dots

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

\int_{0}^{1} e^{x} e^{e^{x}} d x

\int_{1}^{3} (\frac{3}{x ^{2}}) d x

\int_{0}^{2} (\frac{4}{x ^{3}} - \frac{10}{3 x ^{2}}) d x

\int_{1}^{4} 4 x^{3} d x

What is the integral from 0 to 0.8 of e^{-x} ?
The integral from 0 to 0.8 of e^{-x} is 0.55067…