JEE Main20244 Apr 2024Evening ShiftMathematicsLimitsActual

Let f(x)= ₀^x (t+ (1-e^ ) ) d t, x R . Then, _ x 0 f(x) x^3 is equal to

Options

A- 1 6
B2 3
C- 2 3
D1 6

Correct answer

A. - 1 6

Step-by-step solution

_ x 0 f(x) x^3 Using L Hopital Rule. _ x 0 f^ (x) 3 x^2 = _ x 0 x+ (1-e^x ) 3 x^2 (Again L Hopital) Using L.H. Rule aligned & = _ x 0 - [ (1-e^x ) (-e^x ) e^x+ (1-e^x ) e^x ] 6 & =- 1 6 aligned

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