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

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Target Exam

CUET

Subject

-- Mathematics - 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:

$∵ 0 < x < 1\,\, ∴ |ln\, x| = –ln\, x$

Then, $\int\,ln\,x\, dx = – \int\,ln\,.1\,dx$

$= –(x\, ln\, x – x) + c = x + x |ln\, x| + c$