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Question: Evaluate : \(\int _ { a } ^ { b } \frac { | x | } { x }\) dx, a \< b -...

Evaluate : ∫ab∣x∣x\int _ { a } ^ { b } \frac { | x | } { x } dx, a < b -

A

|a| – |b|

B

|b| + |a|

C

|b| – |a|

D

None of these

Answer

|b| – |a|

Explanation

Solution

Let I = dx

Case I : When 0 < a < b

then I = dx = . dx = = b – a

= |b| – |a| … (1)

Case II : When a < 0 < b

then I = –. dx + . dx

= – (0 – a) + (b – 0)

= b + a

= |b| – |a| … (2)

Case III : When a < b < 0

then I = . dx = – (b – a) = – b + a

= |b| – |a| … (3)

It is clear from (1), (2) and (3) we get

dx = |b| – |a|.