Step-by-step Solution

Integrate $w^{\frac{1}{3}}$ from $1$ to $8$

Go!
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Final Answer

$\frac{45}{4}$$\,\,\left(\approx 11.25\right)$

Step-by-step explanation

Problem to solve:

$\int_{1}^{8} w^{\frac{1}{3}}dw$
1

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function, and equals $\frac{1}{3}$

$\left[\frac{3}{4}\sqrt[3]{w^{4}}\right]_{1}^{8}$
2

Evaluate the definite integral

$\frac{45}{4}$

Final Answer

$\frac{45}{4}$$\,\,\left(\approx 11.25\right)$

Problem Analysis

$\int_{1}^{8} w^{\frac{1}{3}}dw$

Main topic:

Definite integrals

Time to solve it:

~ 0.04 seconds