What is the integral from 0 to 1 of 3x^7 ?

The integral from 0 to 1 of 3x^7 is 3/8

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integral from 0 to 1 of 3x^7

\int_{0}^{1} 3 x^{7} d x

\frac{3}{8}

Decimal Notation

0.375

Solution steps

\int_{0}^{1} 3 x^{7} 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^{7} d x

Apply the Power Rule

: [\frac{x ^{8}}{8}]_{0}^{1}

= 3 [\frac{x ^{8}}{8}]_{0}^{1}

Compute the boundaries:

\frac{1}{8}

= 3 \cdot \frac{1}{8}

Simplify

= \frac{3}{8}

\int_{1}^{3} \frac{x ^{2}}{4} d x

\int_{0}^{3} x^{3} - 10 x^{2} + 21 x d x

\int_{- 2}^{1} (- x^{2} + 7) d x

\int_{0}^{2} 2 x^{2} + 2 d x

\int_{- 3}^{x^{2}} (x - 5) (x^{2} + 1) d x

What is the integral from 0 to 1 of 3x^7 ?
The integral from 0 to 1 of 3x^7 is 3/8