What is the integral from 1 to 4 of 4x^3 ?

The integral from 1 to 4 of 4x^3 is 255

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integral from 1 to 4 of 4x^3

\int_{1}^{4} 4 x^{3} d x

255

Solution steps

\int_{1}^{4} 4 x^{3} d x

Take the constant out:

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

= 4 \cdot \int_{1}^{4} x^{3} d x

Apply the Power Rule

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

Compute the boundaries:

\frac{255}{4}

= 4 \cdot \frac{255}{4}

Simplify

= 255

What is the integral from 1 to 4 of 4x^3 ?
The integral from 1 to 4 of 4x^3 is 255