Final Answer
Step-by-step Solution
Specify the solving method
Simplify $\sqrt[3]{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{3}$
Learn how to solve problems step by step online.
$\int_{0}^{1}3\sqrt[3]{x^{2}}dx$
Learn how to solve problems step by step online. Integrate the function 3x^2^1/3 from 0 to 1. Simplify \sqrt[3]{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{3}. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as \frac{2}{3}. Divide 1 by \frac{5}{3}.