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

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a
x33x2sin x+sin 2x+C
b
x33x2sin xcos 2x+C
c
x33x2cos xcos 2x+C
d
None of the above 

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detailed solution

Correct option is D

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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