- #1
kasse
- 384
- 1
Int ((2xe^y)dx + (x^2e^y) dy) from (0,0) to (1,-1)
I get the answer 2/e, while my book says 1/e. Am I right or wrong?
I get the answer 2/e, while my book says 1/e. Am I right or wrong?
kasse said:Int ((2xe^y)dx + (x^2e^y) dy) from (0,0) to (1,-1)
I get the answer 2/e, while my book says 1/e. Am I right or wrong?
kasse said:2e^y*INT(x)dx + x^2*INT(e^y)dy
= e^y*x^2 + x^2*e^y = 2e^y*x^2
= 2*e^(-1) =2/e
A line integral is a type of integration that is done along a curve or a line. It involves finding the area under a curve or the work done along a path.
The equation being solved in this line integral is (2xe^y)dx + (x^2e^y)dy from (0,0) to (1,-1).
A line integral is solved by first parameterizing the curve or line, then finding the limits of integration, and finally using the fundamental theorem of calculus to integrate the given equation.
The limits of integration in a line integral represent the starting and ending points of the curve or line along which the integration is being done. These points determine the path over which the integration is performed and, therefore, affect the final result of the integral.
Yes, line integrals have various applications in physics, engineering, and other fields. They are used to calculate work, displacement, and other physical quantities along a path. They are also used in vector fields to find the flow of a fluid or the flux of a force through a surface.