Integral Calculus Question 176
Question: If $ \int\limits_{-3}^{2}{f(x)dx=\frac{7}{3}} $ and $ \int\limits_{-3}^{9}{f(x)dx=-\frac{5}{6}} $ , then what is the value of $ \int\limits_2^{9}{f(x)dx?} $
Options:
A) $ \frac{-19}{6} $
B) $ \frac{19}{6} $
C) $ \frac{3}{2} $
D) $ -\frac{3}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Value of the integral $ \int\limits_2^{9}{f(x)dx} $ $ =\int\limits_{-3}^{9}{f(x)dx-\int\limits_{-3}^{2}{f(x)dx}} $ ? (i) Given, $ \int\limits_{-3}^{9}{f(x)dx=\frac{-5}{6}} $ and $ \int\limits_{-3}^{2}{f(x)dx=\frac{7}{3}} $ Putting these values in equation (i) $ \int\limits_2^{9}{f(x)dx=\frac{-5}{6}-\frac{7}{3}=-\frac{19}{6}} $
BETA
