Integration By Parts Formula

The branch of calculus in which we come to study integrals, their properties, is called Integral Calculus. We may define an antiderivative of a function f(a) as a function F(a) if F'(a) = f(a) for all a in the domain of f. 

Formula for Integral Calculus

The basic calculus formula and examples are:

Examples of Integral calculus 

Example1:

Find the integral calculus of sin(a) da?

Solution: The function

 ∫

sin(a) da has the integral -cos(a) +c, so it will be written as

  ∫

sin(a) da = -cos(a) +c

Example 2: Find what is 

 ∫ 

cos a + a d(a)

Use sum rule :

 ∫

cos a + a d(a) =

 ∫

cos a da +

 ∫

na d(a)

Writing the integral of each,

= sin a +

 

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