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Deepen Performance Task: Beyond Walls The Congressman of your town will visit your school for the inauguration of the newly constructed building. You are a painter who is famous for designing regions bounded by curves, that is why you are asked to present your geometric pattern design and computations for the cost of paint which will be used by the Principal. Your output will be subject for approval based on the criteria: 1. illustration of design [5 points) 2. accuracy(5 points), 3. exactness of solutions (5 points}, and 4. over-all presentation{5 points], Perform the following: 1. State your proposed function and graph 2. Solve the area of the regions bounded by the two functions 3. Use this ratio to estimate the paint needed and to compute the cost of paint 1 square unit a 10 sq. ft. 1 liter of paint {cost 19200] can cover 12 sq. ft. Discover The Area Bounded by Two Curves We know that when f(x) is nonnegative (not below the x axis) on [a, b], the definite integral Jo f(x)dx can be used to determine the area of a planar region that is bounded by the curve f(x), the x- axis and the vertical lines x = a and x = b. This is illustrated in the figure on the right. We can extend this technique of using the definite integral to determine the area of a planar region bounded by a curve f(x) and another curve g(x). Area Bounded by Two Curves If f(x) and g(x) are two continuous function for which f(x) 2 g(x) on [a, b], then the area bounded by the two functions and the Mi. upper curve vertical line x = a and x = b on [a, b] is b A = S' [f(x) - g(x)]dx 1 90. upper curve Methods for Finding the Area Bounded by Curves in Rectangular Coordinates 1. Vertical Strip Method 2. Horizontal Strip Method A = S'[f(x) - g(x)]dx A = S' [f(y) - 8(y)]dy f ( x ) dy dx 80) fo) 8 ( x ) Where: [a, b]- limit of integration Where: [a, b]- limit of integration dx- length of the strip dy- width of the strip f(x) - g(x)-width of the strip f(v) - g(y)- length of the strip A= fly - goldx - area of the region A = [(() - 8(1)]dx - area of the region