In this blog, we will discuss about the topic definite integration and its importance in various examinations.

Yearly trend

The graph above shows how important this topic is from both JEE-Mains as well as JEE-Advanced point of view. The questions are mostly in single option and even in match the following type questions and thus have a very high weightage in competitive exams.

Topics

Integration basically represents the area covered under a curve. Thus definite integration can be used for finding the area under curves.

int_a^bf(x)dx= F(b)-F(a) where, intf(x)=F(x)+c

Properties of definite integration are very useful as they can solve heavy and scary integrals in just few steps. Let us focus on some of them:

1. int_a^bf(x)dx=-int_b^af(x)dx

2. int_a^bf(x)dx=int_a^cf(x)dx + int_c^af(x)dx

3. int_a^cf(x)dx=int_a^cf(t)dt

4. int_a^cf(x)dx=int_a^cf(a+c-x)dx

5. int_a^(2a)f(x)dx=int_0^af(x)+f(2a-x)dx

Apart from these, let us see Lebnitz theorem whose application is frequently asked in JEE-Advanced:

d/dx int_(g(x))^(h(x))f(x)dt = h'(x)f(h(x))-g'(x)f(g(x))

Just practice once on these concepts and fetch marks very easily. All the best.