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

The integral from-1 to 0 of-xe^{2x} is -(-e^2+3)/(4e^2)

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integral from-1 to 0 of-xe^{2x}

\int_{- 1}^{0} - x e^{2 x} d x

- \frac{- e ^{2} + 3}{4 e ^{2}}

Decimal

0.14849 \dots

Solution steps

\int_{- 1}^{0} - x e^{2 x} d x

Take the constant out:

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

= - \int_{- 1}^{0} x e^{2 x} d x

Apply u-substitution

= - \int_{- 2}^{0} \frac{e ^{u} u}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int_{- 2}^{0} e^{u} u d u

Apply Integration By Parts

= - \frac{1}{4} [e^{u} u - \int e^{u} d u]_{- 2}^{0}

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

= - \frac{1}{4} [e^{u} u - e^{u}]_{- 2}^{0}

Compute the boundaries:

- 1 + \frac{3}{e ^{2}}

= - \frac{1}{4} (- 1 + \frac{3}{e ^{2}})

Simplify

= - \frac{- e ^{2} + 3}{4 e ^{2}}

What is the integral from-1 to 0 of-xe^{2x} ?
The integral from-1 to 0 of-xe^{2x} is -(-e^2+3)/(4e^2)