What is the integral from-2 to 0 of e^{-x} ?

The integral from-2 to 0 of e^{-x} is e^2-1

Popular >

integral from-2 to 0 of e^{-x}

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

e^{2} - 1

Decimal Notation

6.38905 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{0} - e^{u} d u

= \int_{2}^{0} - e^{u} d u

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

= - \int_{0}^{2} - e^{u} d u

Take the constant out:

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

= - (- \int_{0}^{2} e^{u} d u)

Use the common integral:

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

= - (- [e^{u}]_{0}^{2})

Simplify

= [e^{u}]_{0}^{2}

Compute the boundaries:

e^{2} - 1

= e^{2} - 1

\int_{0}^{x} \frac{y}{1 + y ^{4}} d y

\int_{1}^{5} 1 + \frac{1}{x ^{2}} d x

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

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

\int_{0}^{\frac{3}{2} π} ∣ sin (x) ∣ d x

What is the integral from-2 to 0 of e^{-x} ?
The integral from-2 to 0 of e^{-x} is e^2-1