What is the integral from 0 to 1 of 2x^5 ?

The integral from 0 to 1 of 2x^5 is 1/3

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integral from 0 to 1 of 2x^5

\int_{0}^{1} 2 x^{5} d x

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\int_{0}^{1} 2 x^{5} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{1} x^{5} d x

Apply the Power Rule

: [\frac{x ^{6}}{6}]_{0}^{1}

= 2 [\frac{x ^{6}}{6}]_{0}^{1}

Compute the boundaries:

\frac{1}{6}

= 2 \cdot \frac{1}{6}

Simplify

= \frac{1}{3}

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What is the integral from 0 to 1 of 2x^5 ?
The integral from 0 to 1 of 2x^5 is 1/3