Concept explainers
Evaluating a Surface
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Multivariable Calculus (looseleaf)
- Find the area between the curves in Exercises 1-28. x=2, x=1, y=2x2+5, y=0arrow_forwardLet F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces. (0,0,0) to find the flux of F through the The square with corners (1, 1, 1), (1, −1, 1), (−1, 1, 1), and (-1, -1, 1), oriented upward. Hint: Use the fact that this is a face of a cube centered at the origin.arrow_forwardUsing Green's formula, calculate the line integral fv'dz + (z + y)*dy, y°dx where the contour C is the triangle ABD with vertices A (a, 0), B (a, a), D (0, a) YA D(0,a) B(a,a) R A(a,0)arrow_forward
- ntegrate G(x, y, z) = x + y + z over the portion of the plane 2x + 2y + z = 2 that lies in the first octant.arrow_forwardUsing Stoke's Theorem, evaluate c where C is any closed surface enclosing a square region of the xz plane bounded by the lines +5 F = 3zx²i + 4z²k x = ±3, z = " SF.dr wherearrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C.F = (-5x + 2y) i + (6x - 9y) j; C is the region bounded above by y = -5x 2 + 250 and below by y=5x2 in the first quadrantarrow_forward
- Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }arrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forwardIntegrate the function F(x,y,z) = 6z over the portion of the plane x+ y +z= 3 that lies above the square 0arrow_forwardUse Green's Theorem to evaluate the integral | x²ydx + xydy where C is the rectangle with vertices (0, 0), (3, 0), (3, 1) and (0, 1), oriented in the counterclockwise direction.arrow_forwardEvaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forwardUse Green's Theorem to evaluate the line integral Lu+o") dx + (3x+cosy) dy where C is the triangle with vertices (0, 0), (0, 2) and (2, 2) oriented counterclockwise. un O 6 O 8 O 14 O 4 O 10 O 12arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,