MATH 181 Final: m181e1s08
Document Summary
Solution: (a) the region is sketched below. y. 2 (b) the points of intersection are found by plugging y = 2x into x + y2 = 3 and solving for x. x + y2 = 3 x + (2x)2 = 3. 4x2 + x 3 = 0 (4x 3)(x + 1) = 0 x = The corresponding y-values are found by plugging the above x-values into the equation y = 2x. 2 x = 1 : y = 2x = 2( 1) = 2. 1 (c) the formula we use to compute the area of the region is: Area =# d c (right left) dy where c and d are the y-coordinates of the points of intersection of the two curves. y. From the graph we see that the right curve is x = 3 y2 and the left curve is x = The limits of integration are c = 2 and d = area is:
