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

1 Answer

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

 

answered Feb 10, 2013 by meena.p
 
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