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JEE Main20254 Apr 2025Morning ShiftMathematicsDefinite IntegrationActual

The value of _ -1 ^1 (1+ |x|-x ) e^x+( |x|-x ) e^ -x e^x+e^ -x d x is equal to

Options

  1. A3- 2 2 3
  2. B2+ 2 2 3
  3. C1- 2 2 3
  4. D1+ 2 2 3

Correct answer

D. 1+ 2 2 3

Step-by-step solution

aligned & I = _ -1 ^1 (1+ |- x |-(- x ) ) e ^ - x +( |- x |-(- x ) ) e ^ -(- x ) e ^ - x + e ^ -(- x ) dx & I = _ -1 ^1 (1+ | x |+ x ) e ^ - x +( | x |+ x ) e ^ x e ^ x + e ^ x dx & 2 I = _ -1 ^1 (1+ | x |+ x + | x |- x ) ( e ^ x + e ^ - x ) ( e ^ x + e ^ - x ) dx & 2 I = _ -1 ^1(1+ | x |+ x + | x |- x ) dx & 2 I =2 ₀^1(1+ | x |+ x + | x |- x ) dx & 2 I =2 ₀^1(1+ 2 x + 0 ) dx & I = ₀^1(1+ 2 x ) dx = [ x + 2 2 3 x ^ 3 / 2 ]₀^1 & I = 2 2 3 +1 aligned

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