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

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

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integral from 0 to 1 of 3x^5

\int_{0}^{1} 3 x^{5} d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{1} 3 x^{5} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{1} x^{5} d x

Apply the Power Rule

= 3 [\frac{x ^{6}}{6}]_{0}^{1}

Compute the boundaries:

\frac{1}{6}

= 3 \cdot \frac{1}{6}

Simplify

= \frac{1}{2}

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