Calculus Examples

$\int_{0}^{\frac{π}{2}} \cos (x) \sqrt{1 + \sin (x)} d x$

Step 1

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

$\frac{d}{d x} [\int_{0}^{\frac{π}{2}} \cos (x) {(1 + \sin (x))}^{\frac{1}{2}} d x]$

Step 2

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

$0$