Calculus Examples

$\int_{- 6}^{6} \sqrt{36 - x^{2}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{36 - x^{2}}$ as ${(36 - x^{2})}^{\frac{1}{2}}$ .

$\frac{d}{d x} [\int_{- 6}^{6} {(36 - x^{2})}^{\frac{1}{2}} d x]$

Step 2

Once $\int_{- 6}^{6} {(36 - x^{2})}^{\frac{1}{2}} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{- 6}^{6} {(36 - x^{2})}^{\frac{1}{2}} d x$ with respect to $x$ is $0$ .

$0$