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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2010 · Mathematics · Indefinite Integration

If ∫ x^2 x d x=(x^2)/(m) x+(x^3)/(n)+c , then what are the values...

If ∫x2ln⁡xdx=x2mln⁡x+x3n+c\int x^2 \ln x d x=\frac{x^2}{m} \ln x+\frac{x^3}{n}+c, then what are the values of mm and nn respectively? where cc is a constant of integration.

Options

  1. A1/3,−1/91 / 3,-1 / 9
  2. B3,−93,-9
  3. C3,9
  4. D3,3

Correct answer

B. 3,−93,-9

Step-by-step solution

∫x2ln⁡xdx=x3mln⁡x+x3n+c⇒x23ln⁡x−∫1x⋅x33dx=x33ln⁡x+x39+c\begin{aligned} & \int x^2 \ln x d x=\frac{x^3}{m} \ln x+\frac{x^3}{n}+c \\ & \Rightarrow \frac{x^2}{3} \ln x-\int \frac{1}{x} \cdot \frac{x^3}{3} d x=\frac{x^3}{3} \ln x+\frac{x^3}{9}+c \end{aligned} On comparing. m=3,n=−9m=3, n=-9
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