Definite IntegrationHard

Question

The value of integral dx, a < b is :

Options

A.b - a  if  a > 0
B.a - b  if  b < 0
C.b + a  if  a < 0 < b
D.| b | - | a |

Solution

Case-I   0 < a < b
∴  |x| = x
then  dx = b - a
Case- II   a < 0 < b
then  = a + b
Case-III   a < b < 0
then     = a - b
∴  = | b | - | a |

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