Note: Give exact answers where possible (for example, n is exact but 3.142 is approximate). 1. [10 marks] Find the exact length of the curve y = 1 - $, 15 x $ 2. 2. [10 marks] Find the exact length of the curve x = "+m, 1sys2. 3. [10 marks] Find the exact value of the area of the surface obtained by rotating the curve y= atz xs 1about the x-axis. 4. [10 marks] Find the exact area of the surface generated by revolving the curve x = y? + 4, O s y s 2 around the x axis. 5. [10 marks] Given the demand curve D(x) = (x - 6) and the supply curveS(x) = x, find the consumer surplus and the producer surplus. Illustrate by sketching the supply and demand curves and identifying the surpluses as areas. 6. [10 marks] After an 8-mg injection of dye, the readings of dye concentration at 2-second intervals are as shown in the table. Use Simpson's Rule to estimate the cardiac output, giving the appropriate units. 0 2 4 10 12 14 16 18 20 C(t) 0 2.4 5.1 7.8 7.6 5.4 3.9 2.3 1.6 0.7 0