All Questions
124
questions
2
votes
1
answer
67
views
Evaluation of the given line integral
Question: Evaluate $\int_{C}$B.dr along the curve $x^{2}$+$y^{2}$=1,$z$= 1 in the positive direction from (0,1,2) to (1,0,2);given
B= (xz²+y)i+(z-y)j+(xy-z)k
The question itself is easy,but I don't ...
- 33
2
votes
1
answer
72
views
Line integral over two squares
I want to calculate the following integral
$$\oint\limits_{C_1} \oint\limits_{C_2} \frac{\vec {dl_1} \cdot \vec {dl_2}} r,$$
where
The square paths $C_1$ and $C_2$ over which the integration should ...
2
votes
0
answers
87
views
Line integral where $C$ is the boundary of the square -Green's Theorem
I am trying to solve the following problem but I face difficulties with the results. Any suggestion?
The line integral $\int_C y^2 dx - x dy$, where $C$ is the boundary of the square $[-1,1]\times[-1,...
0
votes
1
answer
48
views
Finding parameterization for exponential integrand
I'm currently working on a practice problem for my Calculus III class:
"Evaluate the line integral along the negatively-oriented closed curve C, where C is the boundary of the triangle with ...
0
votes
0
answers
37
views
Line integral over multiple lines by parameterizing the curves
I have solved this problem by setting a relationship between x and y for the 2 lines and got 11. However, when I try solving by the method of parameterization, I come up with 36.
I tried setting $C_1 =...
- 13
0
votes
0
answers
44
views
What is the work done along a quarter circle in a vector field?
What is the work done along a quarter circle in a particular vector field?
To better understand different types of line integrals, I set up the problem below, and request verification:
Let $F$ be a ...
- 4,450
2
votes
0
answers
77
views
Line Integral along a Ellipse over a Scalar field
Given is the Line Integral:
$$\int_C = \sqrt{\frac{a^2y^2}{b^2} + \frac{b^2x^2}{a^2}}ds$$
the Path $C$ is along the border of the ellipse with:
$$\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1$$
and moves ...
- 41
3
votes
0
answers
79
views
Help for evaluating the line integrals with Green's Theorem
Earlier, when I scrolled the Instagram posts I found a mathematical problem uploaded by The Vegan Math Guy like the following because this problem looks interesting to me to be solved. The ...
- 155
2
votes
1
answer
398
views
Stokes' theorem on a triangle
I've been given a question that I'm having trouble figuring out:
Calculate
\begin{equation}
\oint_{T} xydx + yzdy + zxdz
\end{equation}
using Stokes' theorem, where $T$ is the triangle with vertices ...
- 143
1
vote
2
answers
120
views
How to calculate the line integral when the vector field is conservative?
Calculate
$$\int_{\gamma} x^3 dx + (x^3 + y^3)dy$$
where $\gamma$ is the line $y=2-x$ from $(0, 2)$ to $(2, 0)$.
It was my understanding that if the vector field was conservative then the path doesn't ...
- 1,237
3
votes
1
answer
97
views
Calculate flow integral using Stokes's theorem
Calculate the flow integral $$\iint_{Y} \text{curl} (\vec{F}) · \hat{N} dS$$
where $Y$ is part of the sphere $x^2 + y^2 + (z − 2)^2 = 8$ that lies
above the $xy$-plane and $\hat{N}$ is the outward ...
- 1,237
0
votes
1
answer
88
views
What is the integral of y dx around the unit circle?
I'm trying to find $\int y \, dx$ over the unit circle. I'm thinking it should be negative $\pi$, because e.g. in the 1st quadrant, dx is negative and y is positive, so the result is negative there, ...
0
votes
0
answers
24
views
inferring sign of a double integral over a general region D from double integrals of all boxes that lie inside D and containing D
Suppose a double integral
$$
I_{D}:=\iint\limits_D f(x,y) dx dy
$$
over a specific type of region $D=\{(x,y) : x_{\min}\leq x \leq x_{\max}, h_1(x) \leq y \leq h_2(x)\}$. Note that $h_1, h_2$ are ...
- 71
0
votes
1
answer
65
views
Line integral of $r=1+cos(\theta)$
Given
My approach:
since $$r=1+cos(\theta)$$ we get
$$\begin{cases} x=cos(\theta)+cos^2(\theta) \\ y=sin(\theta)+\frac{sin(2\theta)}{2} \end{cases}$$
therefore substituting in the integral gives
$$-\...
- 331
1
vote
2
answers
99
views
Compute the line integral of $x^2 + y^2$ on curve $|x|+|y|=1$
Compute the integral
$$\int_{\gamma} f(x,y)ds$$
where $\gamma=\{|x|+|y|=1\}$ and $f(x,y)=x^2+y^2$
Note, we have not covered any major theorems on evaluating line integrals, which has been presented ...
- 516