What is the integral from 4 to 1 of \sqrt[5]{5x} ?

The integral from 4 to 1 of \sqrt[5]{5x} is -\sqrt[5]{5}((10\sqrt[5]{4})/3-5/6)

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integral from 4 to 1 of \sqrt[5]{5x}

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

- 55 (\frac{10 5 4}{3} - \frac{5}{6})

Decimal

- 4.91877 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{4} 5 5 x d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= - \int_{1}^{4} 55 5 x d x

Take the constant out:

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

= - 55 \cdot \int_{1}^{4} 5 x d x

Apply the Power Rule

: [\frac{5}{6} x^{\frac{6}{5}}]_{1}^{4}

= - 55 [\frac{5}{6} x^{\frac{6}{5}}]_{1}^{4}

Compute the boundaries:

\frac{10 5 4}{3} - \frac{5}{6}

= - 55 (\frac{10 5 4}{3} - \frac{5}{6})

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What is the integral from 4 to 1 of \sqrt[5]{5x} ?
The integral from 4 to 1 of \sqrt[5]{5x} is -\sqrt[5]{5}((10\sqrt[5]{4})/3-5/6)