IIT JEE , AIEEE Forum - Mathematics , Integral Calculus - please help!!!!!!!!!!!!!!!!!!!!!!!!i need to know this!!!!!!!!!!

satish1988

1.can we find antiderivatives of peacewise defined functions when integrating indefinitely?

2.any continuous function has an antiderivative,does the vise versa hold good?

3.can we generalize the fact that if a function is continuous in an interval, we can think of an antiderivative?

4.will any discontinuous function in its domain be an integrable function?
5.what do you mean by an antiderivative?

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iitkgp_bipin

In calculus, an antiderivative, primitive or indefinite integral of a function f is a function F whose derivative is equal to f, i.e., F ? = f. The process of solving for antiderivatives is antidifferentiation (or indefinite integration).

Antiderivatives are related to definite integrals through the fundamental theorem of calculus, and provide a convenient means for calculating the definite integrals of many functions.

They can be used to compute definite integrals, using the fundamental theorem of calculus: if F is an antiderivative of the integrable function f, then:

$\int_a^b f(x)\,dx = F(b) - F(a).$

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