What is the integral from 0 to 2 of 8x^3 ?

The integral from 0 to 2 of 8x^3 is 32

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integral from 0 to 2 of 8x^3

\int_{0}^{2} 8 x^{3} d x

32

Solution steps

\int_{0}^{2} 8 x^{3} d x

Take the constant out:

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

= 8 \cdot \int_{0}^{2} x^{3} d x

Apply the Power Rule

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

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

Compute the boundaries:

4

= 8 \cdot 4

Simplify

= 32

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What is the integral from 0 to 2 of 8x^3 ?
The integral from 0 to 2 of 8x^3 is 32