What is the integral from 0 to 2 of 4x^7 ?

The integral from 0 to 2 of 4x^7 is 128

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integral from 0 to 2 of 4x^7

\int_{0}^{2} 4 x^{7} d x

128

Solution steps

\int_{0}^{2} 4 x^{7} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{2} x^{7} d x

Apply the Power Rule

: [\frac{x ^{8}}{8}]_{0}^{2}

= 4 [\frac{x ^{8}}{8}]_{0}^{2}

Compute the boundaries:

32

= 4 \cdot 32

Simplify

= 128

7^{9 x}

\int (\frac{4}{cos ^{2} ( x )} - \frac{5}{sin ^{2} ( x )}) d x

(\frac{1}{y ^{2}} - \frac{2}{y ^{4}}) (y + 8 y^{3})

\int_{- 2}^{3} \frac{35}{x ^{4}} d x

What is the integral from 0 to 2 of 4x^7 ?
The integral from 0 to 2 of 4x^7 is 128