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AP EAMCET202420 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If 2 1+ x d x=2 |A(x)-B(x)|+C and 0 x 2 then B ( 4 )=

Options

  1. A1 2+3 3
  2. B1 3+2 2
  3. C-1 3+2 2
  4. D2 2+ 2

Correct answer

B. 1 3+2 2

Step-by-step solution

I= 2 1+ x d x I= 2 1+ (x- 2 ) d xI= 1 ( x 2 - 4 ) d x I= ( x 2 - 4 ) d xI=2 | ( x 2 - 4 )+ ( x 2 - 4 ) |+CI=2 | ( x 2 - 4 )- ( 4 - x 2 ) |+C B(x)= ( 4 - x 2 ) B ( 4 )= ( 8 ) Now, ( 2 8 )= 2 8 1- ^2 8 ^2 8 +2 8 -1=0 Let 8 =y y^2+2 y-1=0 y= 2 -1 8 0 8 = 2 -1 B ( 4 )= 2 -1= 2-1 2 +1 = 1 ( 2 +1)^2 = 1 3+2 2

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