What is the integral from 0 to 2 of 5x^4 ?

The integral from 0 to 2 of 5x^4 is 32

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integral from 0 to 2 of 5x^4

\int_{0}^{2} 5 x^{4} d x

32

Solution steps

\int_{0}^{2} 5 x^{4} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{2} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{0}^{2}

= 5 [\frac{x ^{5}}{5}]_{0}^{2}

Compute the boundaries:

\frac{32}{5}

= 5 \cdot \frac{32}{5}

Simplify

= 32

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What is the integral from 0 to 2 of 5x^4 ?
The integral from 0 to 2 of 5x^4 is 32