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What type of object could you best measure using calculus?
Finding the volume of many odd shapes is only possible with integral calculus. Google " volume of revolution. "
Differential and integral calculus sixth edition by Clyde E Love and Earl D.Rainville?
the area bounded by the curve y= e-x, the axes, and the line x-2 is revolved about the x-axis. Find the volume generated
What is the formula for volume in a rectangle?
The formula is: [ Volume = 0 ].A 'plane figure' has no volume. That's any figure that you can draw on paper,and those can't hold water. It takes volume to hold water, and volume takesthree dimensions.
Does a square have volume?
No because volume involves multiplying by a value on the 3rd dimension, and since the length on the 3rd dimension is 0 a square's volume is 0.
How do you get the volume of a square?
The volume of any 2-dimensional object is always zero (0).but if it is not a 2d then it is a 3d and the volume of that would be bxh divided by3.
What is a term used in math'?
volume integral
A derivative is to the rate of change as an integral is to?
A derivative is to the rate of change asan integral is to area/volume.
What is the difference between triple integral and volume integral?
While I searching for the answer to this question, I totally confused. Atlast I reach in one thing that we may compute some volume integrals by using double integral but to evaluate a triple integral we should go through all the three integrals.
What are the applications of volume integral?
This is actually how people approximate real volume of obscured 3D objects.
Is integration a way of calculating the volume of the same function equation with an additional dimension or is it always completely new volume rotated about an axis ie a circle to a sphere?
Geometrically the definite integral from a to b is the area under the curve and the double integral is the volume under the surface. So just taking the integral of a function does not yield the volume of the solid made by rotating it around an axis. An integral is only a solid of revolution if you take an infinite sum of infinitesimally small cylinders that is the disk method or you do the same with shells.
What can you find with triple integrals area or volume?
A triple integral will usually give a measure of volume in 4-dimensional hyper-space.
What is the method to determine the volume of a very small material?
A triple integral should suffice to locate the volume. Provided you can determine a equation to bound the surface.
Applications of integral calculus?
Integration can be used to calculate the area under a curve and the volume of solids of revolution.
You want derivation of cone volume?
This can be done easiest with integrals. Divide the cone into cylinders of very small height, and add up the volume of all the cylinders. Writing that as an integral will immediately give you the volume of the cone. For example, and for the simplifying case that the height is equal to the radius (r), you get the integral from x = 0 to r, of pi*x2. This integral is [(1/3)x3] with an upper limit of r and a lower limit of 0, or simply (1/3)r3.
How do you prove formula for volume of pyramid?
This is easiest done with integral calculus. The basic idea is to divide the pyramid into lots of thin, flat, parallel slabs, calculate the volume of each, and add it up.
What are Line integral Surface integral and Volume integral in simple words?
A line integral is a simple integral. they look like: integral x=a to b of (f(x)). A surface integral is an integral of two variables. they look like: integral x=a to b, y=c to d of (f(x,y)). or integral x=a to b of (integral y=c to d of (f(x,y))). The second form is the nested form. A pair of line integrals, one inside the other. This is the easiest way to understand surface integrals, and, normally, solve surface integrals. A volume integral is an integral of three variables. they look like: integral x=a to b, y=c to d, z=e to f of (f(x,y,z)). or integral x=a to b of (integral y=c to d of (integral z=e to f of f(x,y,z))). the above statement is wrong, the person who wrote this stated the first 2 types of integrals as regular, simple, scalar integrals, when line and surface integrals are actually a form of vector calculus. in the previous answer, it is stated that the integrand is just some funtion of x when it is actually usually a vector field and instead of evaluating the integral from some x a to b, you will actually be evaluating the integral along a curve that you will parametrize to get the upper and lower bounds of the integral. as you can see, these are a lot more complicated. looking at your question tho, i dont think you want the whole expanation on how to solve these problems, but more so what they are and what they are used for, because these can be a pain to solve and there are also several ways to solve them indirectly. line integrals have an important part in physics because they alow us to calculate things such as work that have vector values rather than just scalar values as you can use these integrals to describe a particles path along a curve in a force field. surface integrals help us calculate things like flux, or how fluid flows over a surface. if you want to learn more, look into things like greens theorem, or the divergence theorem. p.s. his definition of a surface integral is acutally how you find the volume of a region
Why do you use integral calculus?
If we have to find the volume of a cylinder then we could imagine as if slices of same size have been mounted one over the other and knowing volume of one piece we could find the entire volume just by multiplying by an integer. But in case of cone, as we put them into thin slices of thickness dx then volume of each would differ as the radii are different for different slices. Hence we need integral calculus with which we could easily get the right formula 1/3 pi r2 h with base radius r and height h
