Question

16 pts) 1. Determine the area of the region between the two curves y=x and y+2x by integrating over the x-axis. Hint: Refer the figure and note that you will have two integrals to solve by splitting the region between the two curves into two smaller regions. lo pl [6 pts) 2. Find the area of the region bounded by the curves y=12 - x, y=vx, and y20

Answer 1

(11 'A (2,8) Given curves are Y= x² y=x2+2x solving o do, we get x3 = x²+2x loloo) B(10) → X(X-2) = 0 =) x ( X-2) (x+1) = 0 + 2 = 0, 2, -1 when x = 0, y = 0 when x=2, y=8 When a=-1, y =-1 :: the intensetting pants are 0 (90), n (28)&B(-17) The required are is A = +18*ede fetare - Przekerd - 12:7-8'-**7*+/6****-27 14 - 41 +10-1-5+1-6-*) 11 + ½ + 4 4 3 + 13 133 4

0 & 9, We Love 2. Given, Y-12-2 0 y=rx and 47,00 ry solving 119.2) 12-x = roc 9 12. Y=12-X => (12- XX =) 144-240 + R² = x = x² 25x+144 = 0 =) (21-16)(x-9) = 0 = r = 16,9 When a=16, y = 4 or y=-4 BUYZO.: Y=4 When X = 9, p = intersecting .. the required area of the sounded region is = 3 Eting point point is (9,3). 12 A q 1] redoel + 12-x)da Ida o 9 هار /nn 123 1"+1123 279 (120)+|(2-12 :)–(12.9-4.JJ |(144-721-(108-81) 135 | 올 2 ? : 33 + = 18 + 1 72-13 2 18 + 13 45 2

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