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Manipal MET2013MathematicsDefinite Integration

aligned & y= _ 1 / 8 ^ ^2 x ⁻¹ t d t+ _ 1 / 8 ^ ^2 x ⁻¹ t d t, & 0 x x / 2 . aligned

Options

  1. AIs the equation of a straight line parallel to the x -axis
  2. BIs the euqation of a straight line which is the bisector of first quadrant
  3. CIs the equation of a straight line which is the bisector of second quadrant
  4. DNone of the above

Correct answer

A. Is the equation of a straight line parallel to the x -axis

Step-by-step solution

Here, we have to prove that, y= constant or derivative of y with respect to x is zero. y= _ 1 / 8 ^ ^2 x ⁻¹ t d t+ _ 1 / 8 ^ ^2 x ⁻¹ t d t (i) aligned & d y d x = ⁻¹ ^2 x 2 x x+ ⁻¹ ^2 x & (-2 x x)=2 x x x-2 x x x & =0 for all x aligned

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