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Considering the images (a),(b),(c),(d),(e),(f) the oriented path is
(a) Negative
(b) Positive
(c) Positive
(d) Zero
(e) Zero
(f) Zero
calculating each quadrant's line integral and symmetry.
In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.
What does a Line integral mean?
- A line integral makes it possible to figure out a surface's area in three dimensions. Numerous situations call for the use of line integrals. They can be used, for instance, in electromagnetics to determine the work done on a charged particle moving along a curve in a force field that is represented by a vector field.
- Path, curvilinear, and curve integrals are other terms for line integrals. There are several uses for line integrals, including electromagnetics, where it is used to calculate the force exerted on a charged particle moving along a curve in a force field created by a vector field.
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An open shape is made up of line segments. In this type of shape there is at least one line segment that is not connected to anything at one of its endpoints, so the shape is not a closed figure. So, I am going to provide four graphs for this problem.
1. Parable
This is given by the curve:
See figure 1.
2. Cubic function.
This function is given by:
see figure 2
3. Quartic function
This curve is given by:
see figure 3
4. Cosine function
This function is given by this equation:
See figure 4.
All these curves are open shapes. So, we can find a new open shape as the sum of all these curves as follows:
See figure 5.
1. Parable
This is given by the curve:
See figure 1.
2. Cubic function.
This function is given by:
see figure 2
3. Quartic function
This curve is given by:
see figure 3
4. Cosine function
This function is given by this equation:
See figure 4.
All these curves are open shapes. So, we can find a new open shape as the sum of all these curves as follows:
See figure 5.