Question

1.Sketch the curve C: y=xe^-x^2 and the line L: y=x+1 for 0 less than or equal to x less than or equal to 2. Hence, determine the area of the region bounded by the curve C, the line L, x=2 and the y-axis.

2.A cannon ball is shot up from the ground at an angle θ to the horizontal. The horizontal distance and the vertical distance from O against time, t, are governed by the following equations respectively:
x = u cos(θ) t
y = u sin(θ) t – 0.5 g t^2
(Hint: u, θ and g are constant parameters)
Determine:

(i) dy/dx in terms of x, u, θ and g; and
(ii) the maximum height of cannon ball attained.