SMN1024: Intermediate Calculus 3. A hydrologist needs to estimate the volume of the water in the approximately circular well as illustrated in Figure 2. The diameters of the well were measured every 5 meter as listed in Table 1. Use the Simpson's Rule to estimate the volume of the water in the well. Table 1 Depth (m) 0 5 10 15 20 25 30 35 40 45 50 55 Diameter (cm) 128.6 125.0 124.3 107.1 92.9 71.4 64.3 67.9 67.1 57. 35.7 25.0 5 m 10 m 15 m 20 m 25 m 30 m 35 m 40 m 45 m 50 m Figure 2 [8 marks] 4. Solve the initial value problem 8 - + 3y =: sine 02 , 8 > 0, y (It) = -5. [12 marks]