A blood vessel is 360 millimeters (mm) long with circular cross sections of varying diameter. The table above gives the measurements of the diameter of the blood vessel at selected points along the length of the blood vessel, where x represents the distance from one end of the blood vessel and B(x) is a twice-differentiable function that represents the diamter at that point.
Distance x(mm) -- Diameter B(x)(mm)
0 -- 24
60 -- 30
120 -- 28
180 -- 30
240 -- 26
300 -- 24
360 -- 26
(a) - Write an integral expression in terms of B9x) that represents the average radius, in mm, of the blood vessel between x=0 and x=360.
(b) - Approximate the value of the answer from part (a) using the data from the chart and a midpoint Riemann sum with three subintervals of equal length. show the comutations.
(c) - Using correct units, explain the meaning of x 125(integral sign)275 ((B(x)/2)^2) dx in terms of the blood vessel.
(d) - Explain why there must be at least one value x, for 0<x<360, such that B''(x)=0
I haven't the SLIGHTEST idea on this problem. This is crucial for me!! Any help woudl be greatly appreciated!! Thanks SOOOOOO much!
Distance x(mm) -- Diameter B(x)(mm)
0 -- 24
60 -- 30
120 -- 28
180 -- 30
240 -- 26
300 -- 24
360 -- 26
(a) - Write an integral expression in terms of B9x) that represents the average radius, in mm, of the blood vessel between x=0 and x=360.
(b) - Approximate the value of the answer from part (a) using the data from the chart and a midpoint Riemann sum with three subintervals of equal length. show the comutations.
(c) - Using correct units, explain the meaning of x 125(integral sign)275 ((B(x)/2)^2) dx in terms of the blood vessel.
(d) - Explain why there must be at least one value x, for 0<x<360, such that B''(x)=0
I haven't the SLIGHTEST idea on this problem. This is crucial for me!! Any help woudl be greatly appreciated!! Thanks SOOOOOO much!
