 # Integral Calculus Formula

The branch of calculus where we get to study about integrals and their properties is known as Integral Calculus. It is a function F(a), which is an antiderivative of a function f(a) if for all in the domain of f, F’(a) = f(a).

## Formula for Integral Calculus

In this page, you’ll see the basic calculus formula and the practice examples.

 $$\begin{array}{l}\int f(a)da\end{array}$$ = F(a) + C, where C is a constant

## Integral Calculus Examples:

Example 1: Find the integral calculus of sin(a) da?

Solution: The function

$$\begin{array}{l}\int\end{array}$$
sin(a) da has the integral -cos(a) + c , so it will be written as
$$\begin{array}{l}\int\end{array}$$
sin(a) da = -cos(a) + c

Example 2: Find what is

$$\begin{array}{l}\int\end{array}$$
cos a + a d(a)

Use sum rule :

$$\begin{array}{l}\int\end{array}$$
cos a + a d(a) =
$$\begin{array}{l}\int\end{array}$$
cos a da +
$$\begin{array}{l}\int\end{array}$$
a d(a)

Writing the integral of each,

= sin a +

$$\begin{array}{l}\frac{a^{2}}{2}\end{array}$$
+ c

Stay tuned to BYJU’S to explore more on other important mathematical formulas.