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JEE Main202528 Jan 2025Morning ShiftMathematicsDefinite IntegrationActual

If _ - 2 ^ 2 96 x^2 ^2 x (1+e^x ) d x= ( ^2+ ), , Z , then ( + )^2 equals

Options

  1. A64
  2. B196
  3. C144
  4. D100

Correct answer

D. 100

Step-by-step solution

aligned & I= ₀^ 2 96 x^2 ^2 x 1+e^x d x & 2 I=2 ₀^ 2 96 x^2 ^2 x d x & I=96 ₀^ 2 x^2 ^2 x d x & =48 ₀^ 2 x^2(1+ 2 x) d x & =2 ^2+48(0-0)-48 ₀^ 2 x 2 x d x & =2 ^2-12 +[0-0]= (2 ^2-12 ) & = ( ^2+ ) & ( + )^2=100 aligned

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