Surface integrals to calculate the area of this figure

In summary, the conversation revolved around using integration to calculate the area of squares and triangles. The speaker mentioned having trouble with solving for squares and not knowing how to type integrals. They also discussed the distance between squares and how it relates to their lengths. The conversation ends with the speaker apologizing for not including the equations section and not knowing how to type integrals.
  • #1
VVS2000
150
17
Homework Statement
My homework is to find the area of the following figure(leaving those two squares)
Relevant Equations
The distance between those two squares is one unit. Please do tell if the figure is not descriptive enough
20200320_164038.jpg

I can find the area of the triangles but can't solve the squares for some reason
 
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  • #2
Sry for not including the equations section, I don't know how to type integrals here
 
  • #3
VVS2000 said:
Sry for not including the equations section, I don't know how to type integrals here
Are you sure you need integration for this?
 
  • #4
Well the assignmet was clear of me using integration
 
  • #5
And the squares are of 1/2 unit length
 
  • #6
VVS2000 said:
Well the assignmet was clear of me using integration
You can, course, use integration to calculate the area of a square or a triangle - just for practice.
 
  • #7
Please post your image right side up.
 
  • #8
One edge of one square is at ##(-0.5, 0)## while the other square has an edge at ##(0.5,0)##, and the total length between them is ##1##.
If you can figure out the distance between ##(-0.5, 0)## and ##(0.5,0)##, do you think that you can deduce something?
20200320_164038.jpg
 
  • #9
I supose all those denominators that look sort of like an ##\alpha## are actually ##2##'s.Your figure shows the inner distance between the squares as ##1## unit and the outer distance between them is ##\frac 1 2 - (-\frac 1 2) = 1## so the squares have sides of length ##0##, so they aren't there.
 
  • #10
VVS2000 said:
Sry for not including the equations section, I don't know how to type integrals here
See the LaTeX tutorial at the top of the page under INFO, Help. :smile:
 

FAQ: Surface integrals to calculate the area of this figure

1. What is a surface integral?

A surface integral is a mathematical concept used in multivariable calculus to calculate the area of a three-dimensional figure. It involves integrating a function over a two-dimensional surface, similar to how a regular integral calculates the area under a curve.

2. How is a surface integral different from a regular integral?

A surface integral involves integrating over a two-dimensional surface, while a regular integral integrates over a one-dimensional curve. Additionally, a surface integral can also involve a vector field, which adds a directional component to the calculation.

3. When would you use a surface integral to calculate area?

A surface integral is typically used when calculating the area of a three-dimensional figure with a curved surface. It is also useful for calculating the flux of a vector field through a surface.

4. What is the formula for calculating a surface integral?

The formula for a surface integral is ∫∫S f(x,y,z) dS, where S is the surface, f(x,y,z) is the function being integrated, and dS represents the differential element of the surface.

5. Are there any applications of surface integrals in real life?

Surface integrals have many real-life applications, such as calculating the surface area of a 3D object for manufacturing purposes, determining the flow of a fluid through a curved pipe, and calculating the electric flux through a charged surface in physics.

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