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Q.

The value of I=∫02πxsin8xsin8x+cos8xdx is equal to

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a

2π2

b

π2

c

π

d

1

answer is B.

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Detailed Solution

2I=∫02πxsin8xsin8x+cos8x+(2π-x)sin8xsin8x+cos8xdx=∫0π4πsin8xsin8x+cos8xdx=∫0π/28πsin8xsin8x+cos8xdx=4π∫0π/2sin8xsin8x+cos8x+cos8xsin8x+cos8xdx=4π·π2=2π2 Therefore, I=π2
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