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

The integral from 1 to 3 of 2x^3 is 40

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integral from 1 to 3 of 2x^3

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

40

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{3} x^{3} d x

Apply the Power Rule

= 2 [\frac{x ^{4}}{4}]_{1}^{3}

Compute the boundaries:

20

= 2 \cdot 20

Simplify

= 40

What is the integral from 1 to 3 of 2x^3 ?
The integral from 1 to 3 of 2x^3 is 40