Definite Integration Question 47
Question: Suppose f is such that $ f(-x)=-f(x) $ for every real x and $ \int _{0}^{1}{f(x)dx=5,} $ then $ \int _{-1}^{0}{f(t)dt=} $
[MP PET 2000]
Options:
A) 10
B) 5
C) 0
D) - 5
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ f(-x)=-f(x) $
We know that, $ \int _{-a}^{a}{f(x)dx=0=\int _{-a}^{0}{f(x)dx+}\int_0^{a}{f(x)dx}} $
$ \Rightarrow \int _{-1}^{0}{f(x)dx+}\int_0^{1}{f(x)dx=0}\Rightarrow \int _{-1}^{0}{f(x)dx=-5} $
$ \Rightarrow \int _{-1}^{0}{f(t)dt=-5} $ .
BETA
