What is the integral from 0 to 1 of 5x^6 ?

The integral from 0 to 1 of 5x^6 is 5/7

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integral from 0 to 1 of 5x^6

\int_{0}^{1} 5 x^{6} d x

\frac{5}{7}

Decimal

0.71428 \dots

Solution steps

\int_{0}^{1} 5 x^{6} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{1} x^{6} d x

Apply the Power Rule

= 5 [\frac{x ^{7}}{7}]_{0}^{1}

Compute the boundaries:

\frac{1}{7}

= 5 \cdot \frac{1}{7}

Simplify

= \frac{5}{7}

What is the integral from 0 to 1 of 5x^6 ?
The integral from 0 to 1 of 5x^6 is 5/7