Q255 / 270 · NDA 2020 · Mathematics

What is the value of $k$ such that integration of $\frac{3 x^2+8-4 k}{x}$ with respect to $x$, may be a rational function?

  • A
    0
  • B
    1
  • Correct answer
    C
    2
  • D
    -2

Solution

$I=\int\left(\frac{3 x^2+8-4 k}{x}\right) \cdot d x$ $\begin{aligned} & =\int 3 x d x+\int \frac{8-4 k}{x} \cdot d x \\ & =\frac{3}{2} x^2+(8-4 k) \cdot \ln (x)+C \end{aligned}$ where $C=$ constant To get integration as rational function, $(8-4 k) \cdot \ln (x)=0 \Rightarrow 8-4 k=0 \Rightarrow k=\frac{8}{4}=2$

Hence, the correct answer is option: 'C'.

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