question_answer

If , then the value of \[\int\limits_{0}^{\pi /2}{f(x)dx}\] is

A) 3         

B) 2/3   

C) 1/3       

D)  0

Correct Answer: C

Solution :

[c] : Applying \[{{C}_{1}}\to {{C}_{1}}-{{C}_{2}}-{{C}_{3}}\], we get \[=3\sin x-4{{\sin }^{3}}x=\sin 3x\] Now,\[\int\limits_{0}^{\pi /2}{\sin 3xdx}=\left[ \frac{-\cos 3x}{3} \right]_{0}^{\pi /2}=\left[ \frac{-0+1}{3} \right]=\frac{1}{3}\]