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AP EAMCET2007MathematicsDefinite Integration

If f(t)= _ -t ^t e^ -|x| 2 d x , then _ t f(t) is equal

Options

  1. A1
  2. B1 2
  3. C0
  4. D-1

Correct answer

A. 1

Step-by-step solution

aligned f(t) & = _ -t ^t e^ -|x| 2 d x & =2 ₀^t e^ -x 2 d x & =- [e^ -x ]₀^t=-e^ -t +1 aligned Now, aligned _ t f(t) & =- _ t e^ -t +1 & =0+1 & =1 aligned

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