logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Integrals
0 votes

Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\sin 2x\;dx\]

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • (i)$ \int \limits_a^b f(x)dx=F(b)- F(a)$
  • (ii)$\int \sin ax=-\frac{1}{a} \cos ax+c.$
  • (iii)$cos 0=1 \qquad cos \pi/2=0$
Given $ I=\int \limits_0^{\pi/4} \sin 2x dx$
 
On integrating we get
 
$-\large\frac{1}{2} [\cos 2x]^{\pi/4}_0$
 
On applying limits we get
 
$-\large\frac{1}{2} [\cos 2.\frac{\pi}{4}-cos 0]$
 
But $\cos \pi/2=0\; and \cos =1$
 
$=-\frac{1}{2}[0-1]=\frac{1}{2}.$
 
$=\frac{1}{2}$

 

answered Feb 10, 2013 by meena.p
 
Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...