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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \limits_0^1 (x^3-x^2-x-1) . \sin x dx$

$(a)\;6(\cos 1 -\sin 1)-1 \\(b)\; \cos 1+ \sin 1-1 \\(c)\; \cos 1-1 \\ (d)\;\tan 1-\cot 1 $
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1 Answer

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$x^3-x^2-x-1=u, \sin x=v$
=> $\int (x^3-x^2-x-1)(-\cos x ) -(3x^2-2x62-1) (-\sin x) +(6x-2)(\cos x)- 6 (\sin x)$
=> $-(x^3-x^2-x-1) \cos x + (3x^2 -2x-1) \sin x + (6x-2) \cos x - 6 \sin x$
=>$6(\cos 1 -\sin 1)-1$
Hence a is the correct answer.
answered Dec 31, 2013 by meena.p
 
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