Definite Integration

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.