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AP EAMCET202318 May 2023Morning ShiftMathematicsDefinite IntegrationActual

_ 1 25 ^3 e^ 3 x x^2 d x=

Options

  1. A- 1 3 (e⁷⁵-e )
  2. B1 3 (e⁵⁰-e²⁵ )
  3. C- 1 3 ( e ⁵⁰- e )
  4. D1 3 (e⁷⁵-e )

Correct answer

D. 1 3 (e⁷⁵-e )

Step-by-step solution

Let I= _ 1 25 ^3 e^ 3 x x^2 d x Let 3 x =t - 3 x^2 d x=d t 1 x^2 d x=- 1 3 d t When x=3 t=1 aligned & x= 1 25 t=75 & I= ₇₅^1 e^t (- 1 3 d t )=- 1 3 [e^t ]₇₅^1 & =- 1 3 [e-e⁷⁵ ] aligned I= 1 3 [e⁷⁵-e ]

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