First slide

Methods of integration

Question

If the primitive of $\frac{1}{f (x)}$ is equal to $\log {f (x)}^{2} + C$ then f(x) is

Moderate

A

x + d
B

$\frac{x}{2} + d$
C

$\frac{x^{2}}{2} + d$
D

x²+ d

Solution

Given that,
$\begin{array}{l} \int \frac{1}{f (x)} dx = \log {f (x)}^{2} + C \\ \Rightarrow \frac{1}{f (x)} = \frac{1}{{f (x)}^{2}} 2 f (x) f^{'} (x) \\ \Rightarrow f^{'} (x) = \frac{1}{2} \\ \Rightarrow f (x) = \frac{x}{2} + d \end{array}$
[where, d is a integration constant]

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