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Q.

The value of ∫−π2π2cos2x1+3x dx

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a

2π

b

4π

c

π4

d

π2

answer is C.

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Detailed Solution

I=∫−π2π2cos2x1+3x dx =∫−π2π2cos2x1+3−x dx since ∫-aaf(x)dx =∫-aaf(-x)dxI=∫−π2π23xcos2x3x+1 dx 2I= ∫-π2π2cos2x1+3x3x+1dx=∫−π2π2cos2x dx=2∫0π2cos2x dx ( since cos2x is even function)=2×12×π2I=π4

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