Given,f(x)=0x2−sin ⁡xcos ⁡x−2sin ⁡x−x201−2×2−cos⁡ x2x−10′ then ∫f(x)dx is equal to 

Given,f(x)=0x2sin xcos x2sin xx2012x2cos x2x10' then f(x)dx is equal to 

  1. A

    x33x2sin x+sin 2x+C

  2. B

    x33x2sin xcos 2x+C

  3. C

    x33x2cos xcos 2x+C

  4. D

    None of the above 

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    Solution:

    We have, 

                       f(x)=0x2sin xcos x2sin xx2012x2cos x2x10f(x)=0sin xx22cos  xx2sin x02x1cos x212x0

    [interchanging rows and columns]

    f(x)=(1)30x2sin xcos x2sin xx2012x2cos x2x10

    [taking (-1) common from each column]

     f(x)=f(x)f(x)=0 f(x)dx=c

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