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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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$\int x \sin x \cos x dx$

$(a)\;\frac{x}{4} \cos 2x-\frac{\sin 2x}{4}+c \qquad(b)\;\frac{-x}{4} \cos 2x+\frac{\sin 2x}{4}+c \qquad(c)\;\frac{-x}{4} \sin 2x + \frac{\cos 2x}{4}+c \qquad (d)\;None$
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1 Answer

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=> $\large\frac{1}{2}$$\int x. \sin 2x dx$
=> $\large\frac{1}{2} .\int x. \frac{(-) \cos 2x}{2} + \frac{1}{2} $$\int 1 \times \large\frac{\cos 2x}{2}$$dx$
=>$\large\frac{-x}{4} $$\cos 2x+\large\frac{\sin 2x}{4}$$+c$
Hence b is the correct answer.
answered Dec 24, 2013 by meena.p
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