Question

EXPERTS!
please explain the concept of integration ​

Answer 1

☑️ CONCEPT OF INTEGRATION :-

Integration is defined as the inverse process of the differentiation. It is also known as antideravative or primitive of the function.

IMPORTANT THEOREMS RELATED TO INTEGRATION :-

• integeral of the product of a constant and a function is equal to the product of the constant and integral of the function.

• the integral of the sum or difference of a finite number of function is equal to the sum or difference of the integrals of various function.

☑️ METHODS OF INTEGRATION :-

• integration by substitution

• integration by parts

• integration by partial fraction

Integration by Substitution

The method of evaluating an integral by reducing into standard form by a proper substitution is called integration by substitution.

NOTE :

We make the substitution for a function whose derivative generally occurs in the integral.

Integration by Parts

When the given function is expressed as a product of two functions of the same variable and we cannot change it to some standard form, then we apply the method known as integration by parts.

AS WE CAN USE THIS FORMULAE IN THIS METHOD :

Integral of the product of two functions = Ist function × Integral of the second function - Integral of (differential of the first function × Integral of the IInd function )...

HERE, we can also choose the Ist function as the function which comes Ist in the word ILATE, where...

I - stands for the inverse trigonometric function

L - stands for the logarithmic function

A - stands for the algebraic function

T - stands for the trigonometric function

E - stands for the exponential function

Integration by Partial Fraction

Integrals can be evaluated by writing down the partial function of the integrand if

(i) Integrand of the form of P(x)/Q(x) where P(x) and Q(x) are the polynomial in x.

(ii) Q(x) has only linear and quadratic factors.

Before writing down the partial fraction of P(x)/Q(x) the highest power of x in the numerator P(x) should be made less than the highest power of Q(x) by dividing P(x) by Q(x).

HOPE IT HELPS ☺