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Question

If g(x)=x0cos4tdt, then g(x+π) equals to

A
g(x)+g(π)
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B
g(x)g(π)
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C
g(x)g(π)
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D
g(x)g(π)
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Solution

The correct option is A g(x)+g(π)
Given :
g(x)=x0cos4tdt
g(x+π)=x+π0cos4tdt=π0cos4tdt+x+ππcos4tdt=g(π)+I
Here I=x+ππcos4tdt
Substitute t=y+πdt=dy
I=x0cos4(π+y)dyI=x0cos4(y)dy=g(x)
So, g(x+π)=g(x)+g(π)

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