INTEGRAL CALCULUS

Ø An integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Ø Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other.

Ø Calculus deals principally with two geometric problems.

(i) The problem of finding SLOPE of the tangent line to the curve, is studied by the limiting process known as differentiation and

(ii) Problem of finding the AREA of a region under a curve is studied by another limiting process called Integration.

Newton-Leibnitz Integral:

Ø Integral calculus is mainly divided into indefinite integrals and definite integrals.

Basic Rules of Integration:

Methods of Integration:

(1) Integration by decomposition into sum or difference.

(2) Integration by substitution.

(3) Integration by parts

(4) Integration by successive reduction.

PROBLEMS

Question 1 :

Question 2 :

Question 3 :

Question 4 :

Question 5 :

Question 6 :

Question 7 :

Question 8 :