Volume integral with 3 formulas mmn 15 3a

In summary, the conversation is about finding the volume enclosed by the planes z=0, x=y, and y^2+z^2=x. The speaker is having trouble visualizing the shape and suggests projecting it onto different planes to build the appropriate integral. However, they admit they are having difficulty drawing the shape and imagining it. They believe that if they could see how the shape looks like, it would be easier to solve the problem.
  • #1
nhrock3
415
0
find the volume inclosed by z=0 x=y and y^2+z^2=x
??

i am having trouble drawing it
i know i should look on th shadow of it on the x-y plane and integrate by it

i can project on every plane i want to and build the integral appropriatly
i jast can't imagine this shape

if i can find out how the shape looks like
then it will solve it very fast
but imaganening a parabaloid cutting x=0 plane and z=0
is very hard thing to draw and imagine
 
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  • #2
Tell us what you get when you project onto each plane?
 
  • #3
thats the problem i don't know how to draw it
 

1. What is a volume integral?

A volume integral is a mathematical concept used in calculus to find the total volume of a three-dimensional region. It involves integrating a function over a given volume to find the total amount of a quantity.

2. What are the three formulas for volume integral?

The three formulas for volume integral are: triple integral, cylindrical coordinates, and spherical coordinates. Each formula is used in different situations depending on the shape and orientation of the given region.

3. How do you solve a volume integral?

To solve a volume integral, you first need to determine the limits of integration for each variable. Then, you integrate the given function over the given volume using one of the three formulas. Finally, you evaluate the integral and get the final answer for the volume.

4. What is the significance of mmn 15 3a in volume integral?

The notation "mmn 15 3a" is commonly used in mathematics to represent a specific problem or question. It may refer to a specific volume or region that needs to be integrated, or it may represent a set of variables or constants used in the problem.

5. In what real-life situations is volume integral used?

Volume integral is used in many real-life situations, such as calculating the volume of a liquid in a container, finding the mass of an object with varying density, and determining the total charge in a given volume for electrical engineering applications. It is also commonly used in physics and engineering to solve problems involving three-dimensional objects.

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