calculus II

posted by .

Suppose R is the region in the plane enclosed by y = x2 and y = 4.
a) Compute the perimeter P and area A of R, and then compute the ratio Q = A/P2.
Note By squaring the perimeter the ratio becomes independent of the units chosen to measure the region.
b) Compute this ratio Q = A/P 2 for these four regions: the region R, a square, a circle, and an equilateral triangle. Draw the figures in increasing order of Q.

  • calculus II -

    I assume you know the formula for the length of a curve in Calculus.
    L = ∫( 1 + (dy/dx)^2 )^(1/2) dx (from left x to right x)

    This is the hard part of the question

    I ended up finding the length of the parabolic curve to be
    L = 2∫(1 + 4x^2)^(1/2) dx from x=0 to x=2

    I ran this through WolFram to get
    http://integrals.wolfram.com/index.jsp?expr=%281%2B+4x%5E2%29%5E%281%2F2%29&random=false
    sub in the values, add on the distance from (-2,4) to (2,4) and you have the perimeter of R

    For the area:
    A = 2∫(4 - x^2) dx from x = 0 to 2
    which you should be able to do quite easily.

    The length of the curve is the only difficult part of the problem.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    f(x)=x^2 - 5x +7 and g(x) 3/x 1) Indicate points of intersection 2) compute the area enclosed by the graphs of f(x) and g(x). 1) (1, 3) , (3, 1) 2)Area = ∫ [1 to 3] [(3/x) - (x^2 - 5x + 7)] dx = [3 ln x - (1/3)x^3 + (5/2)x^2 - …
  2. calculus -- PLEASE HELP!

    Suppose you are trying to evaluate the intergral 2x^3dx and you make the substitution u=x^2. The substitution takes one area and converts it to a different one-in this case a trapezoid with vertical sides. Denote by R the region under …
  3. statistics

    Suppose that you are given a decision situation with three possible state of nature: s1, s2, and s3. The prior probabilities are P(s1) =.1, P(s2) = .6, and P(s3) = .3. With sample information I, P(I|s1) =.15, P(I|s2) = .2, and P(I|s3) …
  4. Calculus - please help!

    Suppose that 0 < c < ¥ð/2. For what value of c is the area of the region enclosed by the curves y = cos x, y = cos(x - c), and x = 0 equal to the area of the region enclosed by the curves y = cos(x - c), x = ¥ð, and y = 0?
  5. pre-calc

    area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three parallel …
  6. Calculus

    Given the vector u=<3,1,1>,v=<-2,0,4>. A) compute the area of the parallelogram determined by u and v . B) compute the vector. UxV
  7. calculus

    Given the vector u=<3,1,1>,v=<-2,0,4>. A) compute the area of the parallelogram determined by u and v . B) compute the vector. UxV
  8. Calculus

    Express the area of the region in the xy-plane enclosed by the curve ((x^(2))/(9))+((y^(2))/(4))=1 in terms of an integral.
  9. Calculus

    (a) Compute the area of the bounded region enclosed by the curve y = e^x, the line y = 12, and the y-axis. (b) How does this area compare with the value of the integral ∫1-12(ln x dx)?
  10. Calculus

    (a) Compute the area of the bounded region enclosed by the curve y = e^x, the line y = 12, and the y-axis. (b) How does this area compare with the value of the integral ∫ from 1 to 12 of (ln x dx)?

More Similar Questions