What is the integral from 1 to 2 of 4x^5 ?

The integral from 1 to 2 of 4x^5 is 42

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integral from 1 to 2 of 4x^5

\int_{1}^{2} 4 x^{5} d x

42

Solution steps

\int_{1}^{2} 4 x^{5} d x

Take the constant out:

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

= 4 \cdot \int_{1}^{2} x^{5} d x

Apply the Power Rule

= 4 [\frac{x ^{6}}{6}]_{1}^{2}

Compute the boundaries:

\frac{21}{2}

= 4 \cdot \frac{21}{2}

Simplify

= 42

What is the integral from 1 to 2 of 4x^5 ?
The integral from 1 to 2 of 4x^5 is 42