• # 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

Solution :

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

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