What is the integral from 0 to 3 of 4xe^{-x} ?

The integral from 0 to 3 of 4xe^{-x} is 4(-4/(e^3)+1)

Popular >

integral from 0 to 3 of 4xe^{-x}

\int_{0}^{3} 4 x e^{- x} d x

4 (- \frac{4}{e ^{3}} + 1)

Decimal Notation

3.20340 \dots

Solution steps

\int_{0}^{3} 4 x e^{- x} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{3} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{0}^{3}

= 4 [- e^{- x} x - \int - e^{- x} d x]_{0}^{3}

\int - e^{- x} d x = e^{- x}

= 4 [- e^{- x} x - e^{- x}]_{0}^{3}

Compute the boundaries:

- \frac{4}{e ^{3}} + 1

= 4 (- \frac{4}{e ^{3}} + 1)

\int_{0}^{\frac{π}{2}} x^{2} y cos (x y^{2}) d x

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

\int_{0}^{π} cos^{3} (5 x) d x

\int_{0}^{1} x \cdot 3 (1 - x)^{2} d x

\int_{- 4}^{5} - x + 2 d x

What is the integral from 0 to 3 of 4xe^{-x} ?
The integral from 0 to 3 of 4xe^{-x} is 4(-4/(e^3)+1)