Work
In Exercises 25–-28, use Green’s Theorem to calculatethe work done by the force F on a particle that is moving counter clockwise around the closed path C.
C: boundary of the region lying between the graphs of
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Bundle: Calculus: Early Transcendental Functions, 7th + Webassign, Multi-term Printed Access Card
- Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z > 0, oriented toward the xz- plane. flux =arrow_forward1) Consider the closed surface: z = h – x^2 - y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux due to È through the surface.arrow_forwardUse Green's theorem for the work done by the force F= (x - y)i + (x + y)j, for the shaded region R of the image YA x² + y²=4 R x² + y² = 1 +arrow_forward
- Consider the function f(x,y) = (e* - x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (1,4) in the direction in which f decreases most rapidly. vector =. (b) Suppose v = 67+3}+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (1,4). What is a?arrow_forwardulus III |Uni Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively oriented curve C, where C is the rectangle with vertices(0,0), (4, 0), (4, 2) and (0, 2).arrow_forwardUse Stokes’ Theorem to evaluate the closed loop line integral F*dr where F(x,y,z) = xi + yj + 3(x^2+y^2)k and C is the boundary of the part of the paraboloid where z = 81 - x^2 - y^2 which lies above the xy-plane and C is oriented clockwise when viewed from above.arrow_forward
- Using Gauss' theorem to calculate the flow of the vector field 3x3 F: F (x, y, z) = (x^2z, 2x^2, 3z^2) exiting the cylinder defined from the relations x ^2+y ^2<=1, 1<= z <= 2.arrow_forward2) Find the work of F = (x² - y² -4,2xy) on the semi-circle of radius 2 centered at the origin starting at (2,0) and ending at (-2,0) oriented counter-clockwise. Before you calculate the circulation do you expect your answer to be positive, negative, or zero? 3arrow_forwardThe vectorfield r^2 shown in (Image 1) Let C be a part of an parabel in the form of y = ax^2 from point A(0,0) to B(1,2) . The given integral is (Image 2) Task is: Find a paramterization of the curve with the use of t, and calculate the integral with the use of definition. Then show that the vectorfield F is conservative, find the potential fucntion and calculate it.arrow_forward
- Use Green's Theorem to find the work done by the force field F(x,y)= (x3-x2y)i+xy2j on a particle that travels in a counter clockise firection on the region bounded by y=x2 and x=y2arrow_forwardCalculate the flow in the field F along the path C. Flow means line integralF = (x - y) i - (x 2 + y 2) j; C is curve from (4, 0) to (-4, 0) on the upper half of the circle x 2 + y 2 = 16 a) (16π-1)/4 b) 16π c) 8π d) - 8πarrow_forwardSuppose that over a certain region of space the electricalpotential V is given by V(x, y, z) = x^2 − 3xy + xyz.(a) Find the rate of change of the potential at P(3,4,5) inthe direction of the vector v= i − j+ k.(b) In which direction does V change most rapidly at P?(c) What is the maximum rate of change at P?arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning