Definite Integration Question 5
Question: If $ \int _{-1}^{4}{f(x)dx}=4 $ and $ \int_2^{4}{(3-f(x))dx=7,} $ then the value of $ \int_2^{-1}{f(x)dx} $ is
Options:
A) 2
B) - 3
C) - 5
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ \int_2^{4}{(3-f(x))dx=7\Rightarrow 6-\int_2^{4}{f(x)dx=7}} $
therefore $ \int_2^{4}{f(x)dx=-1} $ . Now, $ \int_2^{-1}{f(x)dx=-\int _{-1}^{2}{f(x)dx=-[ \int _{-1}^{4}{f(x)dx+\int_4^{2}{f(x)dx}} ]}} $
$ =-[ \int _{-1}^{4}{f(x)dx-\int_2^{4}{f(x)dx}} ]=-(4+1)=-5 $ .
BETA
