Calculus Examples

$\int_{0}^{\sin (x)} \sqrt{t} d t$

Step 1

Take the derivative of $\int_{0}^{\sin (x)} \sqrt{t} d t$ with respect to $x$ using Fundamental Theorem of Calculus and the chain rule.

$\frac{d}{d x} [\sin (x)] \sqrt{\sin (x)}$

Step 2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$\cos (x) \sqrt{\sin (x)}$

Step 3

Reorder the factors of $\cos (x) \sqrt{\sin (x)}$ .

$\sqrt{\sin (x)} \cos (x)$