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NDA2018MathematicsDefinite IntegrationActual

What is ₁^ e x x dx equal to?

Options

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

Correct answer

B. e ^2+1 4

Step-by-step solution

aligned & ₁^ e x x dx = [ x x ^2 2 ]₁^ e - ₁^ e 1 x x ^2 dx & = ( e ^2 2 -0 )- 1 2 ( 1 2 ) ( x ^2 )₁^ e = e ^2 2 - 1 4 ( e ^2-1 )= 2 e ^2- e ^2+1 4 & = e ^2+1 4 aligned

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