Calculus Examples

$\frac{d y}{d x} = \sin (x^{2})$

Step 1

Rewrite the equation.

$d y = \sin (x^{2}) d x$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

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

Step 2.2

Apply the constant rule.

$y + C_{1} = \int \sin (x^{2}) d x$

Step 2.3

$\int \sin (x^{2}) d x$ is a special integral. The integral is the Fresnel integral function.

$y + C_{1} = S (x) + C_{2}$

Step 2.4

Group the constant of integration on the right side as $K$ .

$y = S (x) + K$