Integral Calculus Question 311
Question: If $ f’(x)=\frac{1}{x}+x $ and $ f(1)=\frac{5}{2} $ , then $ f(x)= $
Options:
A) $ \log x+\frac{x^{2}}{2}+2 $
B) $ \log x+\frac{x^{2}}{2}+1 $
C) $ \log x-\frac{x^{2}}{2}+2 $
D) $ \log x-\frac{x^{2}}{2}+1 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=\int_{{}}^{{}}{{f}’(x),dx}=\int_{{}}^{{}}{( \frac{1}{x}+x )},dx=\log x+\frac{x^{2}}{2}+c $ Put $ x=1, $ then $ \frac{5}{2}=0+\frac{1}{2}+c\Rightarrow c=2 $ Therefore, $ f(x)=\log x+\frac{x^{2}}{2}+2. $
BETA
