What is the integral from 0 to 1 of x/(e^{2x)} ?

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

Popular >

integral from 0 to 1 of x/(e^{2x)}

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

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

Decimal

0.14849 \dots

Solution steps

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

Apply Integration By Parts

: [- \frac{1}{2} e^{- 2 x} x - \int - \frac{1}{2} e^{- 2 x} d x]_{0}^{1}

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

\int - \frac{1}{2} e^{- 2 x} d x = \frac{1}{4} e^{- 2 x}

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

Compute the boundaries:

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

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

- 9.8 x^{2} + 2 x + 1

x y^{^{'}} + 5 y = 7 x^{2}

\int_{1}^{2} \frac{4}{2 x + 3} d x

2 (t - 2)

\int \frac{1}{16 x ^{2} - 24 x - 27} d x

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