Definite Integration Question 127
Question: If f is continuous function, then
[Kerala (Engg.) 2005]
Options:
A) $ \int _{-2}^{2}{f(x)dx=\int_0^{2}{[f(x)-f(-x)]dx}} $
B) $ \int _{-3}^{5}{2f(x)dx=\int _{-6}^{10}{f(x-1)dx}} $
C) $ \int _{-3}^{5}{f(x)dx=\int _{-4}^{4}{f(x-1)dx}} $
D) $ \int _{-3}^{5}{f(x)dx=\int _{-2}^{6}{f(x-1)dx}} $
E) $ \int _{-3}^{5}{f(x)dx=\int _{-6}^{10}{f(x/2)]dx}} $
Show Answer
Answer:
Correct Answer: D
Solution:
Since, f is continues function. Let $ x=t-1 $
$ \therefore $ $ dx=dt $ . When $ x=-3\to 5 $ , then $ t=-2\to 6 $
Therefore, $ \int _{-3}^{5}{f(x)dx} $
$ =\int _{-2}^{6}{f(t-1)dt=}\int _{-2}^{6}{f(x-1)dx} $ .
BETA
