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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Paragraph: f(x) satisfies the relation f(x)- ₀^ / 2 x t f(t) d t= x Question: If ₀^ / 2 f(x) d x=3 , then the value of is

Options

  1. A1
  2. B3 2
  3. C4 3
  4. Dnone of these

Correct answer

C. 4 3

Step-by-step solution

aligned & f(x)- x ₀^ / 2 cost f(t) d t= x & f(x)-P x= x & or f(x)=(P+1) x & Where P= ₀^ / 2 t f(t) d t & = ₀^ / 2 cost (P+1) t d t & = (P+1) 2 ₀^ / 2 2 t d t & P= (P+1) 2 P= 2- & f(x)= ( 2- +1 ) x=2 & x=2- & [1,3] & ₀^ / 2 2 2- x d x=3 & = 4 3 aligned

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