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:

integration formula

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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Integration By Parts Formula

Formula for Integral Calculus

The basic calculus formula and examples are:

integration formula

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 +

Other Related Sections

Admissions Open for

Frequently Asked Questions

What is an integral formula?

An integral formula provides a method to evaluate the integral of a function, representing the area under the curve of that function or the accumulation of quantities.

What is the purpose of integral tables?

Integral tables offer precomputed antiderivatives for various functions, simplifying the process of finding integrals for complex or unfamiliar functions.

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