MHT CET202012 Oct 2020Morning ShiftMathematicsDefinite IntegrationActual
_ -5 ⁵ [ e^ x +e^ -x e^ x -e^ -x ] d x=
Options
- A0
- B1
- C3 e⁵
- 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