Integration
1. Express y in terms of x if 
and y passes through the point (4,
) ( x > 0 )
2. A curve has a derivative 
Given that y passes through (8, 8) find the y coordinate when x = 1.
3. Below is part of the curve y = -3 + 4x – x2 Find the roots A and B, and use these to help find the area bounded by the curve and the x – axis between x = 0 and x = B.
y A B x
4. Below is part of the curve y = x3 – 6x2 + 12x – 7
a) Show that y has only one root and find this root.
b) Find the equation of the tangent to y at x = 3
c)
Find the area bounded by the curve and the
tangent at x = 3
y x
