What is the integral from 1 to 3 of-pi/2 3/(\sqrt[3]{x^4)} ?

The integral from 1 to 3 of-pi/2 3/(\sqrt[3]{x^4)} is -(3pi(-3^{2/3}+3))/2

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integral from 1 to 3 of-pi/2 3/(\sqrt[3]{x^4)}

\int_{1}^{3} - \frac{π}{2} \frac{3}{3 x ^{4}} d x

- \frac{3 π ( - 3 ^{\frac{2}{3}} + 3 )}{2}

Decimal

- 4.33500 \dots

Solution steps

\int_{1}^{3} - \frac{π}{2} \cdot \frac{3}{3 x ^{4}} d x

Take the constant out:

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

= - \frac{π}{2} \cdot 3 \cdot \int_{1}^{3} \frac{1}{3 x ^{4}} d x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 π}{2} \cdot \int_{1}^{3} \frac{1}{3 x ^{4}} d x

3 x^{4} = x^{\frac{4}{3}},

assuming

x \geq 0

= - \frac{3 π}{2} \cdot \int_{1}^{3} \frac{1}{x ^{\frac{4}{3}}} d x

Apply the Power Rule

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

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

Compute the boundaries:

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

= - \frac{3 π}{2} (- 3^{\frac{2}{3}} + 3)

Simplify

= - \frac{3 π ( - 3 ^{\frac{2}{3}} + 3 )}{2}

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What is the integral from 1 to 3 of-pi/2 3/(\sqrt[3]{x^4)} ?
The integral from 1 to 3 of-pi/2 3/(\sqrt[3]{x^4)} is -(3pi(-3^{2/3}+3))/2