What is the integral from 0 to 1 of (4xe^x)/3 ?

The integral from 0 to 1 of (4xe^x)/3 is 4/3

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integral from 0 to 1 of (4xe^x)/3

\int_{0}^{1} \frac{4 x e ^{x}}{3} d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{0}^{1} \frac{4 x e ^{x}}{3} d x

Take the constant out:

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

= \frac{4}{3} \cdot \int_{0}^{1} x e^{x} d x

Apply Integration By Parts

= \frac{4}{3} [e^{x} x - \int e^{x} d x]_{0}^{1}

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

= \frac{4}{3} [e^{x} x - e^{x}]_{0}^{1}

Compute the boundaries:

1

= \frac{4}{3} \cdot 1

Simplify

= \frac{4}{3}

What is the integral from 0 to 1 of (4xe^x)/3 ?
The integral from 0 to 1 of (4xe^x)/3 is 4/3