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Question

For any integer n the integral π0ecos2xcos3(2n+1)xdx has the value

A
π
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B
1
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C
0
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D
None of these
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Solution

The correct option is C 0
I=π0ecos2xcos3(2n+1)xdx,nϵZ...(1)=π0ecos2(πx)cos3[(2n+1)(πx)]dxUsing a0f(x)dx=a0f(ax)dxI=π0ecos2xcos3[(2n+1)π(2n+1)x]dxI=π0ecos2xcos3(2n+1)xdx...(2)
Adding (1) and (2) we get
2I=0I=0

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