What is the integral from 1 to 2 of 8x^3 ?

The integral from 1 to 2 of 8x^3 is 30

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integral from 1 to 2 of 8x^3

\int_{1}^{2} 8 x^{3} d x

30

Solution steps

\int_{1}^{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_{1}^{2} x^{3} d x

Apply the Power Rule

= 8 [\frac{x ^{4}}{4}]_{1}^{2}

Compute the boundaries:

\frac{15}{4}

= 8 \cdot \frac{15}{4}

Simplify

= 30

What is the integral from 1 to 2 of 8x^3 ?
The integral from 1 to 2 of 8x^3 is 30