What is the integral from 0 to 1 of x*4x^3 ?

The integral from 0 to 1 of x*4x^3 is 4/5

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integral from 0 to 1 of x*4x^3

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

\frac{4}{5}

Decimal

0.8

Solution steps

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

Take the constant out:

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

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

Simplify

x x^{3} : x^{4}

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

Apply the Power Rule

= 4 [\frac{x ^{5}}{5}]_{0}^{1}

Compute the boundaries:

\frac{1}{5}

= 4 \cdot \frac{1}{5}

Simplify

= \frac{4}{5}

What is the integral from 0 to 1 of x*4x^3 ?
The integral from 0 to 1 of x*4x^3 is 4/5