1. A

    integration of box functions

    integrate minimum of ( x -[x] , -x -[ -x] ) from -2 to 2

    Volume integration

    F=(2x^{2}-3z)i-2xy-4xk Evaluate volume integration of \bigtriangledown \cdot F over a vloume bounded by the planes x=0, y=0, z=0 and 2x+3y+z =4 I got answer as 16/9, is it correct?
  3. J

    Integration by recognition

    Hi, I've been stuck on integration by recognition questions for a long time and can't get my head around them. Any help would be greatly appreciated! Thanks in advance. Here's a couple of examples: 1. Differentiate ln(3-2x) and hence find the antiderivative of 5/(3-2x) 2. Show that...

    Line integration

    Evaluate: \int_{C} (z~dx +x~dy+y~dz) where, C is the intersection of x^{2}+y^{2}=1 and the plane y+z=2. Orient C counter clockwise.

    parameterization in Surface integration

    I want to surface integrate over a surface of the plane S : 2x+3y+6z =12 which lie in the 1st octant. Should I use parameterization, if I should, how?
  6. Z

    requesting for explanation of surface integration

    Evaluate ∫∫ < x, y, -2 > * N dS, where D is given by z = 1 - x^2 - y^2, x^2 + y^2 <= 1, oriented up. Official Answer: - pi Cross Product: \int_{0}^{2\pi} \int_{0}^{1} ( r cos \theta , r sin \theta , -2 ) * ( 2r^2 cos \theta , 2r^2 sin \theta , r ) ~ dr d \theta \int_{0}^{2\pi}...
  7. M


    integrate 1/(4sin^2x-cos2x)

    Volume integration

    What could be the volume of a solid bounded by x = y^{2} 4-x = y^{2} z =0\hspace {2mm} and \hspace {2mm} z=3

    Volume integration

    If I am supposed to do volume Integration over a region bounded by x^{2}+y^{2}=4 z=0 z=3 What limits should I take for x, y and z?
  10. C

    Numerical integration with 3 variables

    I have 3 variables: v, b and h. I know how to calculate v’, b’ and h’. Starting the simulation from an initial condition, I need to calculate v, b and h after a given time using a numerical integrator (say RK4). If I use the simple Euler method, I write; v= v + dt * v’ b= b + dt *...
  11. K

    The proof of calculating area by integration

  12. P

    Integration inequalities

    Trying to prove the following: Let $g(x),l(x),h(x)\geq0$ for all $x\in[a,b]$ with the inequality being strict for at least some $x_1,x_2\in[a,b]$, and let $g$'$(x)$,$l$'$(x)>0$, then $\int_{a}^{b}h(x)g(x)l(x)dx\int_{a}^{b}h(x)dx-\int_{a}^{b}h(x)g(x)dx\int_{a}^{b}h(x)l(x)dx>0$
  13. J

    Integration of 1/sqrt(1/x + c)

    \int \frac{1}{\sqrt{\frac{1}{x} + c}} \text{ d}x Where c is a constant. I've tried integration by substitution but I'm basically failing - I can see it's probably going to end up being trigonometric in some way but can't figure it out. Any advice greatly appreciated!
  14. J

    How do I find the limit of integration ?

    y = 32 - 2x y = 2 + 4x x = 0 about y-axis
  15. F

    split multiplication in integral

    Hi, I've got an equation that looks like this: G = \int_0^X 4\pi (g-1) r^2 \left( 1-\frac{3r}{4R} + \frac{3r^3}{16R^3} \right) dr Now I would like to separate this integral into G = \int_0^X 4\pi (g-1) r^2 dr + Y or G = \int_0^X 4\pi (g-1) r^2 dr * Y where Y does not contain g. Is...
  16. S

    indefinite integration

    integrate the function showing steps.
  17. Z

    Solving cylinder with spherical coordinate triple integration

    Consider the region R within the cylinder x^2 + y^2 <= 4, bounded below by z = 0 and above by z = 2 - y. Assume a mass density = z. Set up and evaluate the integral representing the mass of the solid. This is easy with cylinderical coordinates: \int_{0}^{ 2\pi} \int_{0}^{2}...
  18. H


    Can any show me the steps that were followed to the answer for the attached integration problem?
  19. S


    integrate the function: (cosx)^2/(1+tanx)
  20. E


    Problem 19. An open rectangular box with square ends is fitted with an overlapping lid which covers the top and the front face. Determine the maximum volume of the box if 11m² of metal are used in its construction. Would the answer be 4/5m³?