What is the integral from-7 to 0 of 2/(x^{2/3)} ?

The integral from-7 to 0 of 2/(x^{2/3)} is -6(-1)^{1/3}*7^{1/3}

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integral from-7 to 0 of 2/(x^{2/3)}

\int_{- 7}^{0} \frac{2}{x ^{\frac{2}{3}}} d x

- 6 (- 1)^{\frac{1}{3}} \cdot 7^{\frac{1}{3}}

Solution steps

\int_{- 7}^{0} \frac{2}{x ^{\frac{2}{3}}} d x

Take the constant out:

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

= 2 \cdot \int_{- 7}^{0} \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

: [3 x^{\frac{1}{3}}]_{- 7}^{0}

= 2 [3 x^{\frac{1}{3}}]_{- 7}^{0}

Compute the boundaries:

- 3 (- 1)^{\frac{1}{3}} \cdot 7^{\frac{1}{3}}

= 2 (- 3 (- 1)^{\frac{1}{3}} \cdot 7^{\frac{1}{3}})

Simplify

= - 6 (- 1)^{\frac{1}{3}} \cdot 7^{\frac{1}{3}}

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What is the integral from-7 to 0 of 2/(x^{2/3)} ?
The integral from-7 to 0 of 2/(x^{2/3)} is -6(-1)^{1/3}*7^{1/3}