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Area Bounded by Curves

This text explores the concept of computing the area of regions bounded by curves, specifically using integration with respect to x and y. It outlines two scenarios: The first involves a region R bounded above by y = g(x) and below by y = f(x), with defined vertical limits. The second scenario describes how to determine the area between x = f(y) and x = g(y), with horizontal limits. Additionally, it presents problems where the graphs of the functions are not provided, requiring the calculation of areas using given equations such as x = 2y^2 and y = x^2 - 2x + 1.

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Area Bounded by Curves

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  1. Area Bounded by Curves sin x cos x

  2. Area Bounded by Curves(Integrating w.r.t. x) Let f and g be continuous functions. Let R be the region bounded above by y = g(x), below by y = f (x), on the left by x = a and on the right by x = b. Then R has area

  4. Area Bounded by Curves(Integrating w.r.t. y) Let f and g be continuous functions. Let R be the region bounded on the right by x = g(y), on the left by x = f (y), below by y = c and above by y = d. Then R has area

  6. Problems Where The Graph Isn’t Given Find the area of the region enclosed by the curves. • x = 2y2 x = 2 – y2 • y = x2 – 2x + 1 y = 4 – x2

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