Application of CALCULUS[level 1 sample problem]

Q.A curve 'C' passes through (2, 0) and the slope at (x, y) as . Find the equation of the curve. Find the area bounded by curve and x-axis in fourth quadrant. A. According to question slope of curve C at

Soln is
	y = x(x + 1) + 3 + C (x + 1)	........(1)

As the curve passes through (2, 0),

	0 = 2.3 + 3 + C.3
	c = -3
Eqn. (1) becomes	y = x (x + 1) + 3 - 3x - 3
	y = x2 - 2x	........(2)

which is the required eqⁿ of curve.
This can be written as (x - 1)² = (y + 1)

[Upward parabola with vertex at (1, -1), meeting x -axis at (0, 0) and (2, 0)]

Area bold by curve and x-axis in fourth quadrant is as shaded region in adjacent fig. given by