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JEE Main202523 Jan 2025Morning ShiftMathematicsIndefinite IntegrationActual

Let I (x)= d x (x-11)^ 11 13 (x+15)^ 15 13 . If I (37)- I (24)= 1 4 ( 1 ~b ^ 1 13 - 1 c ^ 1 13 ), b , c N , then 3( ~b + c ) is equal to

Options

  1. A22
  2. B39
  3. C40
  4. D26

Correct answer

B. 39

Step-by-step solution

aligned & I(x)= d x (x-11)^ 11 13 (x+15)^ 15 13 & Put x-11 x+15 =t 26 (x+5)^2 d x=d t & I(x)= 1 26 d t t^ 1 / 13 = 1 26 t^ 2 / 13 2 / 13 aligned aligned & I ( x )= 1 4 ( x -11 x +15 )^ 2 / 13 + C & I (37)- I (24)= 1 4 ( 26 52 )^ 2 / 13 - 1 4 ( 13 39 )^ 2 / 13 & = 1 4 ( 1 2^ 2 / 13 - 1 3^ 2 / 13 ) & = 1 4 ( 1 4^ 1 / 13 - 1 9^ 1 / 13 ) & b =4, c =9 & 3( ~b + c )=39 aligned

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