# integration

1. ### integration of box functions

integrate minimum of ( x -[x] , -x -[ -x] ) from -2 to 2
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. ### 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...
4. ### 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.
5. ### 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. ### requesting for explanation of surface integration

Evaluate âˆ«âˆ« < 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. ### integration

integrate 1/(4sin^2x-cos2x)
8. ### 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
9. ### 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. ### Numerical integration with 3 variables

I have 3 variables: v, b and h. I know how to calculate vâ€™, bâ€™ and hâ€™. 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 * vâ€™ b= b + dt *...

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12. ### 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. ### 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. ### How do I find the limit of integration ?

y = 32 - 2x y = 2 + 4x x = 0 about y-axis
15. ### 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. ### indefinite integration

integrate the function showing steps.
17. ### 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. ### Integration

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

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

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 11mÂ² of metal are used in its construction. Would the answer be 4/5mÂ³?