A) \[\int_{0}^{1}{f(x)\,dx}\]
B) \[\int_{0}^{2}{f(x)\,dx}\]
C) \[\int_{0}^{n}{f(x)\,dx}\]
D) \[n\int_{0}^{1}{f(x)\,dx}\]
Correct Answer: C
Solution :
Let \[I=\int_{0}^{1}{f(k-1+x)dx}\] Þ \[I=\int_{k-1}^{k}{f(t)\,dt,}\]where \[t=k-1+x\]Þ \[I=\int_{k-1}^{k}{f(x)dx}\] \[\therefore \,\,\,\sum\limits_{k=1}^{n}{\int_{k-1}^{k}{f(x)dx=\int_{0}^{1}{f(x)dx+\int_{1}^{2}{f(x)dx+.....+\int_{n-1}^{n}{f(x)dx}}}}}\] \[=\int_{0}^{n}{f(x)\,dx}\].You need to login to perform this action.
You will be redirected in
3 sec