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AP EAMCET202422 May 2024Evening ShiftMathematicsDefinite IntegrationActual

If M = ₀^ t 1+t^3 d t and N = _ - ^ e^ 2 t t 1+e^ 3 t d t , then

Options

  1. AN =2 M
  2. BN = M
  3. CN =3 M
  4. DN =- M

Correct answer

D. N =- M

Step-by-step solution

M = ₀^ t 1+t^3 d t, ~N = _ - ^ t e^ 2 t 1+e^ 3 t d t Let t=e^ - x d t=e^ - x d x M =- _ ^ - -x e^ -x d x 1+e^ -3 x = _ ^ - x e^ -x e^ 3 x 1+e^ 3 x d x=- _ - ^ x e^ 2 x 1+e^ 3 x d x Let x=t M =- _ - ^ te ^ 2 t 1+ e ^ 3 t dt =- N

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