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NDA2018MathematicsDefinite IntegrationActual

What is ₀^ e ^ x x d x equal to?

Options

  1. Ae ^ +1 2
  2. Be ^ -1 2
  3. Ce ^ +1
  4. De ^ +1 4

Correct answer

A. e ^ +1 2

Step-by-step solution

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

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