calculus

posted by .

Find the area of the region in the first quadrant enclosed by the coordinate axes and graph of x^3+y^3=1.

  • calculus -

    Isnt the height of the function (1-x^3)^1/3 ?

    so integrate INT (height)dx from x=0to1

    Having a graph(graphing calc) will help understand.

  • calculus -

    Is it possible to do it by hand? how would I do it by a graphing calculator?

  • calculus -

    The graphing calculator is to graph the function, so you understand what your integral is supposed to do.

    Sure, you can graph it by hand.

  • calculus -

    I cannot find a closed-form solution for the integral in my Tables of Integrals, but the integral can be obtained quite accurately and easily using Simpson's-rule numerical integration. At x values of 0,0.25, 0.5. 0.75 and 1, the values of the function are:
    1, 0.995, 0.957, 0.833, and 0
    Using the Simpson's Rule formula, I get 0.707 for the integral. Higher accuracy can be obtained by breaking up the 0 to 1 range of integration into larger number of slices. I used four (five data points).

  • calculus -

    I haven't learned the Simpson's Rule formula yet.

  • calculus -

    Substitute x = y^1/3 to express it in terms of the Beta function. The integral can then be expressed as:

    1/3 Gamma(4/3)Gamma(1/3)/Gamma(5/3) = 0.883319375...

    Gamma(x) = (x-1)! and most calculators will evaluate it correctly for fractional values of x.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Which has more area, the region in the first quadrant enclosed by the line x+y=1 and the circle x^2+y^2=1, or the region in the first quadrant enclosed by the line x+y=1 and the curve sqrt(x)+sqrt(y)=1?
  2. calculus

    Find the area and dimensions of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed i nthe region enclosed by the graphs of f(x)=18-x^2 and g(x)=2x^2-9.
  3. Calculus 1

    Let f be the function given by f(x)=3sqrt(x-2). A) On the axes provided sketch graph of f and shade the region R enclosed by the graph f, the x-axis, and the vertical line x=8 (already completed just mentioned it for part B.) B) Find …
  4. Calculus

    4. Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed by the graphs of f(x) = 18 – x^2 and g(x) = 2x^2 – 9.
  5. calculus

    Let R be the region in the first quadrant that is enclosed by the graph of y = tanx, the x-axis, and the line x = π/3 h. Find the area of R i. Find the volume of the solid formed by revolving R about the x-axis
  6. calculus

    Sketch the region in the first quadrant enclosed by y=6/x, y=2x, and y=12x. Decide whether to integrate with respect to x or y. Then find the area of the region.
  7. calculus

    Sketch the region in the first quadrant enclosed by y=6/x, y=2x, and y=.5x. Decide whether to integrate with respect to x or y. Then find the area of the region. need final area as answer please, and step would be helpful also if you …
  8. calculus

    R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b > 0. Find the value of b so that the area of the region R is 288 square units.
  9. Calculus 2

    Sketch the region in the first quadrant enclosed by y=7/x, y=2x, and y=x/2. Decide whether to integrate with respect to x or y. Then find the area of the region.
  10. calculus

    R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

More Similar Questions