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AP EAMCET20227 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual

_ - ^ ²⁰²² x 1+(2022)^x d x=

Options

  1. A(2022) ! 2²⁰²²((1011) !)^2
  2. B( 2022 1011 )
  3. C( 2022 1011 ) 2¹⁰¹¹
  4. D(2022) ! (1011) ! 2²⁰²²

Correct answer

A. (2022) ! 2²⁰²²((1011) !)^2

Step-by-step solution

I= _ - ^ ²⁰²² 1+(2022)^x d x ...(i) I= _ - ^ ²⁰²² x (2022^x . (202 Z^x+1 . d x ...(ii) On adding Eqs. (i) and (ii), 2 I= _ - ^ ²⁰²² x d x I= ₀^ ²⁰²² x d x=2 ₀^ / 2 ²⁰²² x d x = 2²⁰²² 2022 ! 1011 !(2022-1011) ! = 2022 ! 2²⁰²²((1011) !)^2

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