Calculus Examples

$\int_{0}^{1} \frac{1}{\sqrt{x}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{d}{d x} [\int_{0}^{1} \frac{1}{x^{\frac{1}{2}}} d x]$

Step 2

Once $\int_{0}^{1} \frac{1}{x^{\frac{1}{2}}} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{0}^{1} \frac{1}{x^{\frac{1}{2}}} d x$ with respect to $x$ is $0$ .

$0$