Calculus

posted by .

Use Green's theorem to evaluate the integral:
y^(2)dx+xy dy
where C is the boundary of the region lying between the graphs of y=0,
y=sqrt(x), and x=9

  • Calculus -

    Using the definition, we have
    P = y^2
    Q = xy

    and the integral becomes

    ∫[0,9]∫[0,√x] (∂Q/∂x - ∂P/∂y) dy dx
    = ∫[0,9]∫[0,√x] (y - 2y) dy dx
    = ∫[0,9]∫[0,√x] -y dy dx
    = ∫[0,9] -x/2 dx
    = -x^2/4 [0,9]
    = -81/4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot ! 1) For the green's theorem, Q: Using Green's theorem, evaluate the line integral F(r).dr counterclockwise …
  2. Calculus

    Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, …
  3. Multivariable Calculus - Green's Theorem

    Compute the line integral of F = <X^3, 4X> along the path from A to B. The path from A to B is not closed, it starts at A which has coordinates (-1,0) goes to (1,0) then goes up to (1,1) then left to (-2,1) then down to (-2,-1) …
  4. Calculus

    Use the shell method to set up, but do not evaluate, an integral representing the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4x-x^2 about the line x=6. I had the shell radius as (6-x) …
  5. Calculus

    Use Green's theorem to evaluate the integral: y^(2)dx+xy dy where C is the boundary of the region lying between the graphs of y=0, y=sqrt(x), and x=9
  6. Calculus

    Use Green's theorem to evaluate the integral: y^(2)dx+xy dy where C is the boundary of the region lying between the graphs of y=0, y=sqrt(x), and x=9
  7. calc

    use green's theorem to evaluate the integral of x^2dy where C is the boundary of the rectangle with vertices (0,0),(2,0),(2,3),(0,3) oriented counterclockwise. the answer is 12. can someone please explain
  8. Calculus check

    The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but …
  9. calculus

    a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i …
  10. Math

    Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] …

More Similar Questions