Calculus Examples

$\int_{\frac{π}{6}}^{\frac{π}{3}} \sec (x) t g (x) \sqrt{\sec (x) + 1} d x$

Step 1

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

$\frac{d}{d x} [\int_{\frac{π}{6}}^{\frac{π}{3}} \sec (x) t g (x) {(\sec (x) + 1)}^{\frac{1}{2}} d x]$

Step 2

Once $\int_{\frac{π}{6}}^{\frac{π}{3}} \sec (x) t g (x) {(\sec (x) + 1)}^{\frac{1}{2}} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{\frac{π}{6}}^{\frac{π}{3}} \sec (x) t g (x) {(\sec (x) + 1)}^{\frac{1}{2}} d x$ with respect to $x$ is $0$ .

$0$