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8.4 Area Between Curves (dx) Name Mastery Check #1 Calculus - Calculator Allowed Date: Period: Find the area of the region bounded by the following curves. Show the integral set up, then you may use a calculator. 1. y = 2x2 + 4x+3, y= -2x - 4, x= -1, x = 0 |2. y = x2 + 1, y = 5 3. y = Vx, y = 3x+z 4. Let R be the region bounded by the graphs 5. Set up the integral(s) to that represent the bounded y =6 - x2 and y = 2x + 3 as shown in the figure. region. Do not solve. If the line x = k divides R into two regions of equal y = x -2, y = - 2, y = 4 -x2 area, what is the value of k?8.6 Area - Multiple Intersections Name: Calculus - Calculator Allowed Mastery Check #1 Date: Period: The given functions create boundaries for multiple regions. 1. y = (x - 1)3, y = x-1 2. y = 10x - x2, y = 16, x = 0 a. Find the x-values of the points of intersection, and a. Find the x-values of the points of intersection, and label them from smallest to largest as A, B, and C. label them from smallest to largest as A, B, and C. A = A= B = C = C = b. Set up integrals b. Set up integrals 3. The figure shows the graph of y = 2 cos(x), and the line y = V3, for - ~ S x -. Write a set of integrals that represents the sum of all the areas of the shaded regions. Use exact values for your boundaries, not rounded decimals. HIN