Target Exam

CUET

Subject

Maths. Section B1

Chapter

Definite Integration

Question:

$|ln\, x|\, dx$ equals $(0 < x < 1)$

Options:

$x - x |ln\, x| + c$

$x |ln\, x| – x + c$

$x + |ln\, x| + c$

$x – |ln\, x | + c$

Correct Answer:

$x - x |ln\, x| + c$

Explanation:

$\int |\ln x| \, dx,\quad 0

$\ln x < 0 \Rightarrow |\ln x| = -\ln x$

$= \int -\ln x \, dx$

$= -\left(x \ln x - x\right)$

$= x - x\ln x$

The value is $x - x\ln x + C$.