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Manipal MET2011MathematicsDefinite Integration

Let I₁= _ ^ - x f( x) d x, I₂= _ x f( x), d x ^ - f( x) d x , then I₂ is equal to

Options

  1. A2 I₁
  2. BI₁
  3. C2 I₁
  4. D2 I₁

Correct answer

C. 2 I₁

Step-by-step solution

Since, I₁= _a^ -a x f( x) d x aligned & = _a^ -a ( -x) f( ( -x)) d x & = _a^ -a ( -x) f( x) d x & = _a^ -a f( x) d x-I₁ 2 I₁ & = I₂ I₂ & = 2 I₁ aligned

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