What is the integral from 1 to 32 of 6/5 x^{1/5} ?

The integral from 1 to 32 of 6/5 x^{1/5} is 63

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integral from 1 to 32 of 6/5 x^{1/5}

\int_{1}^{32} \frac{6}{5} x^{\frac{1}{5}} d x

63

Solution steps

\int_{1}^{32} \frac{6}{5} x^{\frac{1}{5}} d x

Take the constant out:

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

= \frac{6}{5} \cdot \int_{1}^{32} x^{\frac{1}{5}} d x

Apply the Power Rule

= \frac{6}{5} [\frac{5}{6} x^{\frac{6}{5}}]_{1}^{32}

Compute the boundaries:

\frac{105}{2}

= \frac{6}{5} \cdot \frac{105}{2}

Simplify

= 63

What is the integral from 1 to 32 of 6/5 x^{1/5} ?
The integral from 1 to 32 of 6/5 x^{1/5} is 63