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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let F, F^ , F^ be continuous in [0 . , In 2] and f(0)=0, f^ (0)=3, f( 2)=6, f^ ( 2)=4 and ₀^ 2 e^ -2 x f(x) d x=3 then ₀^ 2 e^ -2 x f^ (x) d x is

Options

  1. A10
  2. B13
  3. C12
  4. Dnone of these

Correct answer

B. 13

Step-by-step solution

₀^ 2 e^ -2 x f^ (x) d x= [e^ -2 x f^ (x) ]₀^ 2 +2 ₀^ 2 e^ -2 x f^ (x) d x= [ 1 4 f^ ( 2)-3 ]+2 [e^ -2 x f(x)+2 e^ -2 x f(x) d x ]₀^ 2 =13

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