Test Index

NDA Math Definite Integrals

Show Para Hide Para

For the next four (4) items that follow :

Consider the integral

I_m = \int\limits_{0}^{\pi} \frac{\sin 2mx}{\sin x} dx

where m is a positive integer.

[NDA I 2015]

© examsnet.com

Question : 49 of 62

Marks: +1, -0

What is

I_2+I_3

4
2
1
0

Solution:

Integrating, we get

I=I_2+I_3\int\limits_{0}^{\pi}\frac{\sin 4x+\sin 6x}{\sin x}dx

I=\int\limits_{0}^{\pi}\frac{2\sin 5x\cos x}{\sin x}dx

I=\int\limits_{0}^{\pi}\frac{2\sin 5(\pi-x)\cos(\pi-x)}{\sin(\pi-x)}dx

=-\int\limits_{0}^{\pi}\frac{2\sin 5x\cos x}{\sin x}dx

2I=0

I=0

© examsnet.com

Go to Question:

Prev Question

Next Question