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Basic methods on calculating the area under and between curves. 1. Sketch the area. 2. Determine the boundaries a and b, 3. Set up the definite integral, 4. Integrate Instructions: In solving the below problems; illustrate or draw the curves (5 points), then, calculate the area (5 points). Show all the calculations. 1. Find the area of the region enclosed by the following curves: y = e", y= x' - 1, x =-1 and x =1. 2. Find the area in the first quadrant bounded by f (x) = 4x - x' and the X-axis. 3. Find the area enclosed by r = 4cos20. 4. Find the area enclosed by r? = 16sin20