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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Given a function f: R R defined as f(x)= [ array ll x, & x / 2 array . If f(x)=a ₀^ / 2 |x-t| t d t+b x+c , then:

Options

  1. A2 a+1=0
  2. B2 b-1=0
  3. C2 c-1=0
  4. D8 a b c-1=0

Correct answer

C. 2 c-1=0

Step-by-step solution

f(x)= [ array lc x, & x / 2 array =a ₀^ / 2 |x-t| t d t+b x+c . If x 2 , 1=a x ₀^ / 2 t d t-a ₀^ / 2 t t d t+b x+c c-a=1 and a+b=0 a= -1 2 ; b=c= 1 2

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