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JEE Main202523 Jan 2025Evening ShiftMathematicsArea Under CurvesActual

If the area of the region (x, y):-1 x 1,0 y a+ e ^ |x| - e ^ -x , a 0 is e ^2+8 e +1 e , then the value of a is :

Options

  1. A8
  2. B7
  3. C5
  4. D6

Correct answer

C. 5

Step-by-step solution

aligned & y [0, a+e^ |x| -e^ -x ] & (i) If x 0 y (0, a+e^x- 1 e^x ) & if x aligned & Area =(a)+ ₀^1 (a+e^x-e^ -x ) d x= e^2+8 e+1 e & =a+ . (a x+e^x+e^ -x ) |₀ ^1=e+8+ 1 e & =a+ (a+e+ 1 e -2 )=e+ 1 e +8 & 2 a-2=8 a=5 aligned

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