Question about finding the area between two curves

However, this method only applies to real-valued functions. For complex-valued functions, the concept of area is not well-defined as the graph lies in 4 dimensions.
  • #1
Sinister
33
0
my question might be simple but my professor didn't really explain this..
how do you know what function to subtract from what to find the area between the two graphs..
i know you use integrals of f(b)-g(a)
and f(b) is the function that is above g(a)
but how do you find it out for complex functions?
 
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  • #2
The graph of a complex valued map lies in 4 dimensions & hence area is out of place.
 
  • #3
what...?
 
  • #4
complex as in complicated functions sorry ! not complex numbers :P
 
  • #5
Sinister said:
my question might be simple but my professor didn't really explain this..
how do you know what function to subtract from what to find the area between the two graphs..
i know you use integrals of f(b)-g(a)
and f(b) is the function that is above g(a)
but how do you find it out for complex functions?
If y = f(x) is above the graph of y = g(x) for all x such that a <= x <= b, then the area between the two graphs is
[tex]\int_a^b [f(x) - g(x)]dx[/tex]
 

1. How do you find the area between two curves?

To find the area between two curves, you need to first graph the two curves and determine the points of intersection. Then, you can use the definite integral to calculate the area between the two curves. This involves finding the antiderivatives of the two functions and subtracting the smaller antiderivative from the larger one.

2. What is the formula for finding the area between two curves?

The formula for finding the area between two curves is the definite integral of the difference between the two functions. This can be written as: A = ∫(f(x) - g(x)) dx, where f(x) and g(x) are the two functions and A is the area between them.

3. Can you find the area between two curves if they do not intersect?

No, you cannot find the area between two curves if they do not intersect. In order to calculate the area, the two curves must intersect and form a bounded region. If the two curves do not intersect, there is no bounded region and therefore no area between them.

4. What is the difference between finding the area between two curves and finding the area under a curve?

Finding the area between two curves involves calculating the area of the region bounded by two curves. On the other hand, finding the area under a curve involves calculating the area of the region between the curve and the x-axis. This can also be done using the definite integral, but the limits of integration will be different.

5. Can you use the area between two curves to find the volume of a solid?

Yes, you can use the area between two curves to find the volume of a solid. This can be done by rotating the region between the two curves around a specified axis and using the method of cylindrical shells or disks to calculate the volume. The area between the two curves will then serve as the cross-sectional area of the solid.

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