What is the integral from 0 to 1 of 8x^{-1/5} ?

The integral from 0 to 1 of 8x^{-1/5} is 10

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integral from 0 to 1 of 8x^{-1/5}

\int_{0}^{1} 8 x^{- \frac{1}{5}} d x

10

Solution steps

\int_{0}^{1} 8 x^{- \frac{1}{5}} d x

Take the constant out:

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

= 8 \cdot \int_{0}^{1} x^{- \frac{1}{5}} d x

Apply the Power Rule

: [\frac{5}{4} x^{\frac{4}{5}}]_{0}^{1}

= 8 [\frac{5}{4} x^{\frac{4}{5}}]_{0}^{1}

Compute the boundaries:

\frac{5}{4}

= 8 \cdot \frac{5}{4}

Simplify

= 10

\int_{0}^{5} t d t

\int_{2}^{4} x^{2} - 2 d x

\int_{- 1}^{2} x^{2} - 1 d x

\int_{- x}^{x} x^{2} + y^{2} d y

\int_{- 1}^{1} e^{- ∣ x ∣} d x

What is the integral from 0 to 1 of 8x^{-1/5} ?
The integral from 0 to 1 of 8x^{-1/5} is 10