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Manipal MET2017MathematicsDefinite Integration

_ -1 / 2 ^ 1 / 2 d x (1-x^2 )^ 1 / 2 is equal to

Options

  1. A3
  2. B4
  3. C2
  4. D0

Correct answer

A. 3

Step-by-step solution

Let I= _ -1 / 2 ^ 1 / 2 d x (1-x^2 )^ 1 / 2 Again, let f(x)= 1 (1-x^2 )^ 1 / 2 gathered f(-x)= 1 (1-x^2 )^ 1 / 2 = f(x) I=2 ₀^ 1 / 2 d x (1-x^2 )^ 1 / 2 = [2 ⁻¹ x 1 ]₀^ 1 / 2 gathered =2 ⁻¹ 1 2 =2 6 = 3

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