Line
is the same for each parametric representation of C.
(i)
(ii)
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus, Early Transcendentals
- Example Let F = xy? i+ xy j be a vector field in 2-space. Evaluate $. xy? dx + xy? dy where C is the boundary of the triangle with vertices (0,2),(3,2), and (3,5). (3,5) y+2 (0,2) (3,2) y=2 Example Let C be the curve sketched below and F(x,y, 2) = 3xy i+ 3zj+ 5x R. The straight line on the xy-plane is given by the equation 2x + 3y = 6 and the curve on the yz-plane has an equation of z= 4- y?. Find S. F dř. (00.4) (02,0) (3,0,0), 2x+3y=6arrow_forwardFlux of the radial field Consider the radial vector field F = ⟨ƒ, g, h⟩ = ⟨x, y, z⟩. Is the upward flux of the field greater across the hemisphere x2 + y2 + z2 = 1, for z ≥ 0, or across the paraboloid z = 1 - x2 - y2, for z ≥ 0?Note that the two surfaces have the same base in the xy-plane and the same high point (0, 0, 1). Use the explicit description for the hemisphere and a parametric description for the paraboloid.arrow_forwardHow do you do #3arrow_forward
- D part onlyarrow_forwardQuestion: Find The Outward Flux Of The Vector Field F(x,y,z) = X2i + Y2 J + Z2k Through The First Octant Portion Of The Cylinder X2+y2=49, 3... 5. Find the outward flux of the vector field F(x,y,z) = x²i + y²j + z’k through the first octant portion of the cylinder x2+y?=49,3 < z< 8. (Hint: A parametric form may be helpful.)arrow_forwardHow do you sketch a vector field in R? given by a function F(x, y) ? Typically you look at a grid and at each point on the grid on the plane you draw a very small vector in the direction given by the function F(x, y). You draw vectors like crazy on a grid on the plane You look at the function F(x, y) and then you decide a random point on the plane where you will place these vectors, typically you draw vectors long as if they were very small you will be unable to see them. At each point in R², you assign an arbitrary vector.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning