- #1
bugatti79
- 794
- 1
Homework Statement
Find area of curve using area formula of Greens theorem
Homework Equations
r(t)=(t-sin t) i +(1- cos t ) j for 0 <= t <= 2 pi. The curve is y = sin x
The Attempt at a Solution
Do i let x(t)=t...?
No.bugatti79 said:Homework Statement
Find area of curve using area formula of Greens theorem
Homework Equations
r(t)=(t-sin t) i +(1- cos t ) j for 0 <= t <= 2 pi. The curve is y = sin x
The Attempt at a Solution
Do i let x(t)=t...?
Greens Theorem is a theorem in vector calculus that relates the line integral of a two-dimensional vector field over a closed curve to the double integral over the region enclosed by the curve.
Greens Theorem can be used to calculate the area of a curve by converting the problem into a line integral over the boundary of the region, which can then be solved using the fundamental theorem of calculus.
The main advantage of using Greens Theorem is that it can simplify complex area calculations by converting them into line integrals, which can often be easier to solve. It also allows for the calculation of areas using a wider range of coordinate systems.
Greens Theorem is commonly used in physics, engineering, and mathematical modeling to calculate various physical quantities such as flux, work, and potential energy.
Greens Theorem can only be applied to closed curves in two-dimensional space, and it may not be applicable for calculating areas in certain complex or irregular shapes. It also requires a good understanding of vector calculus and its principles.