What is the integral from-1 to 2 of 5x^{1/3} ?

The integral from-1 to 2 of 5x^{1/3} is 5(3/(2^{2/3)}-3/4)

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integral from-1 to 2 of 5x^{1/3}

\int_{- 1}^{2} 5 x^{\frac{1}{3}} d x

5 (\frac{3}{2 ^{\frac{2}{3}}} - \frac{3}{4})

Decimal

5.69940 \dots

Solution steps

\int_{- 1}^{2} 5 x^{\frac{1}{3}} d x

Take the constant out:

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

= 5 \cdot \int_{- 1}^{2} x^{\frac{1}{3}} d x

Apply the Power Rule

: [\frac{3}{4} x^{\frac{4}{3}}]_{- 1}^{2}

= 5 [\frac{3}{4} x^{\frac{4}{3}}]_{- 1}^{2}

Compute the boundaries:

\frac{3}{2 ^{\frac{2}{3}}} - \frac{3}{4}

= 5 (\frac{3}{2 ^{\frac{2}{3}}} - \frac{3}{4})

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What is the integral from-1 to 2 of 5x^{1/3} ?
The integral from-1 to 2 of 5x^{1/3} is 5(3/(2^{2/3)}-3/4)