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Definite integral is generally considered to be a tough topic by students. It must be studied after one is thorough with the concepts of indefinite integrals. The topic is flooded with formulae related to change of limits etc. and hence demands consistent practice. It is an important component of the IIT JEE Mathematics syllabus and so students cannot dare to skip this topic. It not only requires learning of all important formulae but also requires a good speed with thorough knowledge of integration.
Integration means summation. Integration originated during the course of finding the area of a plane figure. Integration is the reverse of differentiation it is also called as the antiderivative.
Methods of Integration
Substitution
Integration by partial fractions
By parts
Euler substitution
Reduction method
If the area between two bounding values of x on the graph, lies above the x-axis; its sign is taken to be positive. If the area between two bounding values of x on the graph, lies below the x-axis; its sign is taken to be negative. This is known as Area Under the Curve. The area under a curve between two points can be found by doing a definite integral between the two points.
To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b.
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