A) Equal to \[2a\]
B) Equal to \[3a\]
C) Independent of \[a\]
D) None of these
Correct Answer: C
Solution :
Consider the function \[g(a)=\int_{a}^{a+T}{f(x)dx}\] \[=\int_{a}^{0}{f(x)dx+\int_{0}^{T}{f(x)dx+\int_{T}^{a+T}{\,\,f(x)dx}}}\] Putting \[x-T=y\] in last integral, we get \[\int_{T}^{a+T}{f(x)dx=\int_{0}^{a}{f(y+T)dy=\int_{0}^{a}{f(y)dy}}}\] Þ \[g(a)=\int_{a}^{0}{f(x)dx+\int_{0}^{1}{f(x)dx+\int_{0}^{a}{f(x)dx}}}\]\[=\int_{0}^{T}{f(x)dx}\] Hence g is independent of a.
You need to login to perform this action.
You will be redirected in
3 sec
