Calculus Examples

$\int_{1}^{32} \sqrt[5]{x} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x}$ as $x^{\frac{1}{5}}$ .

$\frac{d}{d x} [\int_{1}^{32} x^{\frac{1}{5}} d x]$

Step 2

Once $\int_{1}^{32} x^{\frac{1}{5}} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{1}^{32} x^{\frac{1}{5}} d x$ with respect to $x$ is $0$ .

$0$