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NDA2015MathematicsDefinite IntegrationActual

If 0 a b , then _a^b |x| x d x is equal to

Options

  1. A| b |-| a |
  2. B| a |-| b |
  3. C| b | | a |
  4. D0

Correct answer

A. | b |-| a |

Step-by-step solution

aligned & _a^b |x| x d x & when x 0 & _a^b x x d x & _a^b(1) d x & =[x]_a^b & =|b|-|a| & when x 0 ; as 0 a b ; x will not lie between a and b & so & b a |x| x d x=0 for x 0 & a aligned

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