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MHT CET202012 Oct 2020Morning ShiftMathematicsDefinite IntegrationActual

_ -5 ⁵ [ e^ x +e^ -x e^ x -e^ -x ] d x=

Options

  1. A0
  2. B1
  3. C3 e⁵
  4. D2 e⁵

Correct answer

A. 0

Step-by-step solution

aligned Let f(x)=& e^ x +e^ -x e^ x -e^ -x =& e^ x + 1 e^ x e^ x - 1 e^ x = e^ 2 x +1 e^ 2 x -1 and f(-x)= e^ -x +e^ x e^ -x -e^ x = 1 e^ x +e^ x 1 e^ x -e^ x = 1+e^ 2 x 1-e^ 2 x f(x)=-f(x) aligned Thus f(x) is an odd function. _ -5 ⁵ e^ x +e^ -x e^ x -e^ -x d x=0

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