Calculus Examples

$\int \sin (x^{2}) d x$

$\int \sin (x^{2}) d x$ is an antiderivative of $\sin (x^{2})$ , so by definition $\frac{d}{d x} [\int \sin (x^{2}) d x]$ is $\sin (x^{2})$ .

$\sin (x^{2})$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$