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Question

If I=x0[sint] dt, where x(2nπ,(2n+1)π), nN and [] denotes the greatest integer function, then the value of I is

A
nπ
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B
(n+1)π
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C
2nπ
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D
(2n+1)π
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Solution

The correct option is A nπ
Let I=x0[sint]dt
I=2nπ0[sint] dt+x2nπ[sint] dt

We know that the period of [sint] is 2π, so using
nT0f(x)dx=nT0f(x)dxI=n2π0[sint]dt+x2nπ[sint]dtI=nπ0(0) dt+2ππ(1) dt+x2nπ(0) dtI=nπ

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