What is the integral from 0 to 4 of 2x^3 ?

The integral from 0 to 4 of 2x^3 is 128

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integral from 0 to 4 of 2x^3

\int_{0}^{4} 2 x^{3} d x

128

Solution steps

\int_{0}^{4} 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_{0}^{4} x^{3} d x

Apply the Power Rule

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

Compute the boundaries:

64

= 2 \cdot 64

Simplify

= 128

What is the integral from 0 to 4 of 2x^3 ?
The integral from 0 to 4 of 2x^3 is 128