Integral Calculus Question 187
Question: If $ \int{\frac{dx}{f(x)}=\log {{{f(x)}}^{2}}+c} $ , then what is $ f(x) $ equal to?
Options:
A) $ 2x+\alpha $
B) $ x+\alpha $
C) $ \frac{x}{2}+\alpha $
D) $ x^{2}+\alpha $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] We check from the given options one by one. Options [a] and [b] do not satisfy. We check option (c). Let $ f(x)=\frac{x}{2}+\alpha $
$ \therefore \int{\frac{dx}{\frac{x}{2}+\alpha }}=\int{\frac{2dx}{(x+2\alpha )}} $ $ =2\log (x+2\alpha )+c_1=\log {{(x+2\alpha )}^{2}}+c_1 $ $ =\log {{( \frac{x}{2}+\alpha )}^{2}}+\log 2^{2}+c_1 $ $ =\log {{( \frac{x}{2}+\alpha )}^{2}}+c $
BETA
