Question 3 [(2+ 4) +7+7 =20 marks] (a). It is well known that the rate of flow can be found by measuring the volume of blood that flows past a point in a given time period. The volume I of blood flow through the blood vessel is V = | 2avr dr where v= K( R' -r? ) is the velocity of the blood through a vessel. In the velocity of the blood through a vessel, K is a constant, the maximum velocity of the blood, R is a constant, the radius of the blood vessel and / is the distance of the particular corpuscle from the center of the blood vessel. () If R= 0.30 cm and v =(0.30-3.33r?) cm/s, find the volume. (ii) Construct and develop a general formula for the volume I' of the blood flow. [Verify your answer by MATHEMATICA and attach the printout of the commands and output] Page | 2 JK (b). Find the area of the region enclosed by the graphs of f (x) = x and g(x) =x +2x. [Verify your answer by MATHEMATICA and attach the printout of the commands and output] (c). Find the area of the region enclosed by the graphs of y = - and y =4-x. [Verify your answer by MATHEMATICA and attach the printout of the commands and output]