(I know it looks like a lot but it's just 10 questions)
(part 1 [It also explains my situation]:

(If your willing to do this part along with part 1, you can take a break and do it tomorrow if you want, I don't want to force all this math on someone all at one, if there kind enough to help me)

1. What is the area bounded by y=x^2 and y=3x?

2. The region R is bounded by the axis, x = 2, and y = x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x = 2
(choices) (

3. Refer to the graph and information: An ant is crawling on a straight wire. The velocity, v(t), of the ant at time 0 <or= t <or= 8 is given in the graph. Note: The graph on 0 <or= r <or= 2 is a semi-circle (half-circle).
Given the following velocity curve, at which time (t) is the speed of the ant greatest?

4. An ants position during an 8 second time interval is shown by the graph below. What is the total distance the ant traveled over the time interval 2<=t<=8?
What is the total distance traveled by the ant over the time interval 2<=t<=8?

5. An ant is crawling on a straight wire. The velocity, v(t), of the ant at time 0<=t<=8 is given in the graph. Note: The graph on 0<=t<=2 is a semi-circle.
What is the total distance traveled by the ant over the time interval 0<=t<=8?

6. The average value of the function g(x)=3^cosx on the closed interval [-pi, 0] is:

7. Find the length of the arc defined by f(x) = (1/3)x^(3/2) on the interval from [0,5].

8. The temperature over a given period is:
Estimate the average temperature from 0<=t<=8 using the left endpoints of four equal subintervals
50° F
35° F
32.75° F
26° F
26.4° F

9. A solid has, as its base, the circular region in the xy-plane bounded by the graph of x^2+y^2=4. Find the volume of the solid if every cross section by a plane perpendicular to the x-axis is a quarter circle with one of it's radii in the base.

10. The change in the momentum of an object (Δ p) is fiven by the force, F, acting on the object multiplied by the time interval that the force was acting: Δ p = F Δ t.
If the force (in newtons) acting on a particular object is given by F(t) = cost, what's the total change in momentum of the object from time t=5 until t=7 seconds.
0.402 newton*sec
0.708 newton*sec
0.909 newton*sec
1.416 newton*sec
1.616 newton*sec

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asked by George
  1. #1. The curves intersect at (0,0) and (3,3) so the area is
    ∫[0,3] 3x - x^2 dx

    #2. using discs of thickness dy,
    v = ∫[0,4] πr^2 dy
    where r = 2-x = 2-√y
    v = ∫[0,4] π(2-√y)^2 dy
    Using shells of thickness dx,
    v = ∫[0,2] 2πrh dx
    where r=2-x and h=y=x^2
    v = ∫[0,2] 2π(2-x)x^2 dx

    #3. Surely you can read a graph ...

    #4. the distance traveled is just twice the sum of the heights of the two triangles. Think about it.

    #5. the distance is just the area of the semi-circle and the two triangles

    #6. as always, the average value is the area divided by the width:
    ∫[-π,0] 3^cosx dx / π ≈ 1.325

    #7. using the formula you have,
    s = ∫[0,5] √(1+(y')^2) dx = ∫[0,5] √(1+(√x/2)^2) dx = 1/4 ∫[0,5] √(x+4) dx

    #8. figure the area using 4 rectangles of width 2. Then divide by 8

    #9. It sounds like the quarter circle has radius y, so the area is 1/4 πy^2 = π/4 (4-x^2). Stacking up all those thin plates of thickness dx, and using the symmetry of the region,
    v = 2∫[0,2] π/4 (4-x^2) dx

    #10. you can approximate Δp = FΔt by
    dp = F dt
    p = ∫F dt
    over the interval of interest

  2. Could you please check these for me?

    1. 9/2
    2. I understand!
    3. Would it be 4?
    4. 3(2) + -1(2) = 4?
    5. 4+(pi/2)
    6. 1.325
    7. I got 3.16 but this is not an answer choice?
    8. 32.75
    9. 8pi/3
    10. This one is a bit confusing for me. How do I get the force?

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    posted by George

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