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
- AIs the equation of a straight line parallel to the x -axis
- BIs the euqation of a straight line which is the bisector of first quadrant
- CIs the equation of a straight line which is the bisector of second quadrant
- 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