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

The integral from 0 to 2 of ye^{x-y} is ye^{-y}(e^2-1)

Popular >

integral from 0 to 2 of ye^{x-y}

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

y e^{- y} (e^{2} - 1)

Solution steps

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

Take the constant out:

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

= y \cdot \int_{0}^{2} e^{- y + x} d x

e^{- y + x} = e^{- y} e^{x}

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

Take the constant out:

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

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

Use the common integral:

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

= y e^{- y} [e^{x}]_{0}^{2}

Compute the boundaries:

e^{2} - 1

= y e^{- y} (e^{2} - 1)

\int_{0}^{5} (x^{3} - x) d x

\int_{2}^{3} 4 sin (\frac{π}{3} x) d x

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

\int_{x}^{2} 1 + sin (t) d t

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

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