MATH 1680 Lecture 1: Lecture 35

Area Between Curves For problems 6-8 graph the enclosed region and find the area of the region. Note that you can use computational aids to do the graphs, but I do expect to see a sketch in your homework! 6. The area bounded by y-2-e-3x,y=2+3e-x, x=-1 and x=2. Note that these curves don't intersect inside this interval so you don't need to worry about that for this problem. 7. The area bounded by y-(x-2 ), y = 4-x2, x =-1 and x = 4 . 8. The area bounded by x =y2-y-6 and x = 4-y.

Find the area of the region bounded by the graph of the function f(x) = x2 + 2, the x-axis and the lines x = -2 to x = 2.

2. Consider the region R bounded by the graph-2z+ 1, the z-axis, and the vertical lines z = 0 an x=6. (a) Sketch the graph on an appropriate interval, and indicate the region R clearly. (b) Find the area of region R using the definition area = 'lino Σ/(right.)&z.