Question:
The line integral of function \(F = yz\hat{i}\), in the counter clockwise direction, along the circle x2 + y2 = 1 at z = 1 is
The line integral of function \(F = yz\hat{i}\), in the counter clockwise direction, along the circle x2 + y2 = 1 at z = 1 is
Updated On: Mar 12, 2025
- -2π
- -π
- π
- 2π
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct answer is(B): -π
Was this answer helpful?
0
0
Top Questions on Line integrals and Green's theorem
- Let \(C\) be the positively oriented boundary of the domain bounded by the curves \(y=2x^{2}\) and \(y^{2}=4x\). Then the value of the line integral \[ \oint_{C} (2y^{2}+2xy+4y)\,dx + (x^{2}+4xy+8x)\,dy \] is equal to:
- GATE XE - 2025
- Engineering Mathematics
- Line integrals and Green's theorem
- The line integral of the vector field \( \vec{F} = (zx, xy, yz) \) along the boundary of the triangle with vertices (1,0,0), (0,1,0), (0,0,1) anticlockwise, when viewed from the point (2,2,2) is
- AP PGECET - 2024
- Engineering Mathematics
- Line integrals and Green's theorem
- Which one of the following functions is differentiable at $z=0$ but NOT differentiable at any other point in the complex plane $\mathbb{C}$?
- GATE XE - 2023
- Engineering Mathematics
- Line integrals and Green's theorem
- Consider the two-dimensional vector field $\vec{F}(x,y)=x\,\hat{i}+y\,\hat{j}$, where $\hat{i}$ and $\hat{j}$ denote the unit vectors along the $x$-axis and the $y$-axis, respectively. A contour $C$ in the $xy$-plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral \[ \oint_{C} \vec{F}(x,y)\cdot(dx\,\hat{i}+dy\,\hat{j}) \] is ________________.
- GATE EC - 2022
- Engineering Mathematics
- Line integrals and Green's theorem
Let \( \Gamma \) denote the boundary of the square region \( R \) with vertices \( (0,0), (2,0), (2,2), (0,2) \), oriented in the counter-clockwise direction. Then \( \int_{\Gamma} (1 - y^2) dx + x \, dy = \underline{\hspace{1cm}}. \)
- GATE MA - 2021
- Calculus
- Line integrals and Green's theorem
View More Questions
Questions Asked in CUET PG exam
- Arrange the following events related to India-Pakistan relations in a chronological order.
A. Operation Gibraltar
B. Kargil War
C. Karachi Agreement
D. Indus Water Treaty
- CUET (PG) - 2025
- India’s Foreign Policy
- What is the number of radial nodes for a 4f orbital?
- CUET (PG) - 2025
- Atomic Structure
- Fill in the blank with the appropriate word from the options given below: He, as well as his friends, ............ denied entry to the stadium.
- CUET (PG) - 2025
- Subject Verb Agreement
Find the next two terms of the series:
The given series is: \( A, C, F, J, ? \).(A) O
(B) U
(C) R
(D) V
Choose the correct answer from the options given below:
- CUET (PG) - 2025
- Letter Series
- The infection that develops in admitted patients after more than 48 hours of hospitalization is termed as ____________ infection.
- CUET (PG) - 2025
- Epidemiology
View More Questions