advertisement

Math 165 – Quiz 10B, area between curves – solutions Problem 1 Find the area of the region between the x-axis and the curves given by y = 3x − x2 , x + y = 4. Solution The two given curves meet at (2, 2). There are also the points (0, 0) and (4, 0) where these curves intersect the x-axis. We split the given region into the part above [0, 2] and the part above [2, 4]. The first part has area 2 Z 2 10 3 2 1 3 2 = . 3x − x dx = x − x 2 3 3 0 0 The second part has area Z 2 4 1 4 − x dx = 4x − x2 2 4 = 8 − 6 = 2. 2 So the total area equals 16/3. Alternative: it was possible to solve this using a dy-integral. However, in this Quiz 10B, it was not really practical or useful, so please see the solution to Quiz 10A for an example.