Integrals For Class 12

We are already aware that if a function f(x) is differentiable in an interval I, then its derivative f’(x) exist at each point of I. Now the question arises, if the derivative of the function is known to us, is it possible to obtain the function. The answer to this question is yes. By the means of Integration ( or antiderivative of a function) it is possible to obtain the original function.

The Integral calculus is of the two form, namely

(i) Indefinite Integral

(ii) Definite Integral

In an indefinite integral, the range of the function is not defined, thus the value of the function obtain is followed by a constant value ‘c.

Whereas in a definite integral, the range of the function is well defined, thus it gives a well defined function.

The integration is denoted by \((\int)\). Let us have a look on various antiderivative of functions.

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Practise This Question

10 tan1x dx=