2. (a) Find the area below the curve: Between the limits 0 and 0.5 y = x²(0.5-x) dx 3

Q1: Find the area bounded by: The curve y=4x-x and the lines y=0, x=1 and x=3.

Let f(x) = 9 + 2x². (a) Estimate the area under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. R3 = Improve your estimate by using six rectangles. R6 = Sketch the curve and the approximating rectangles for R2. y y y y 15 15 15 15 10 10- 10 10 5 5 5 X 0-1 1 1 O-1 1 2 D-1 1 2 Sketch the curve and the approximating rectangles for Rg. y y y 15 15 15 15 10 10 10 10 5 5 5 2 O0-1 -0.5 0.5 1 1.5 -0.5 0.5 1 1.5 2 @O-1 -0.5 O-1 0.5 1.5 2 -1 -0.5 0.5 1 1.5 2

Find the area between the curves. y=x2 − 9x + 3  and  y=x2 + 9  from  x=0  to  x=6