MY NOTES ASK YOUR TEACHER Consider the following video. The arc of the parabola y = x- from (1,1 ) to (2, 4 ) is rotated about the y-axis. Find the area of the resulting surface. y1 (2, 4 ) Click here to view the transcript. EXAMPLE y = The arc of the parabola 2x2 from (3, 18) to (6, 72) is rotated about the y-axis. Find the area of the resulting surface. SOLUTION 1 y = 2x- and dy = dx Using we have, from this formula, S = 2xx ds - 2xx / 1 + (dx) dx = 2x xV1 + 16x2 dx. U = 1+ Substituting 16x2, we have du = dx. Remembering to change the limits of integration, we have S = Vudu 1577 76 145 SOLUTION 2 Using x = and dx dy we have S = 2nx ds = 2xx\\/1 + (dx ) day = 27 1 + 1 dy -2 VBy + I dy 16145 Vudu ( where u = 1 + 8y) (as in Solution 1) Need Help? Read It3. [-/0.18 Points] DETAILS SCALCET9 8.XP.2.004. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis. X =1 y (a) about the x-axis dy (b) about the y-axis dy O Need Help? Read It Submit