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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2020 · Mathematics · Indefinite Integration

What is the value of k such that integration of (3 x^2+8-4 k)/(x)...

What is the value of kk such that integration of 3x2+8−4kx\frac{3 x^2+8-4 k}{x} with respect to xx, may be a rational function?

Options

  1. A0
  2. B1
  3. C2
  4. D-2

Correct answer

C. 2

Step-by-step solution

I=∫(3x2+8−4kx)⋅dxI=\int\left(\frac{3 x^2+8-4 k}{x}\right) \cdot d x=∫3xdx+∫8−4kx⋅dx=32x2+(8−4k)⋅ln⁡(x)+C\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}$wherewhereC=constantTogetintegrationasrationalfunction,constant To get integration as rational function,(8-4 k) \cdot \ln (x)=0 \Rightarrow 8-4 k=0 \Rightarrow k=\frac{8}{4}=2$
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