Scalar Surface Integral. A scalar surface integral is I| (7, y, =) dS = ||, s (r(u, v)) ||r. x ro|| du dv where f is a scalar function defined on the parametric surface r(u, v). 1. Evaluate the surface integral where S is the part of the plane r+ y + 2z = 2 in the first octant. Vector Surface Integral (Flux Integral). Suppose F is a continuous vector field on an oriented surface S with unit normal vector n. The surface integral of F over S is F. dS = = || F· (r„ × r,) du dv F.ndS 2. Evaluate the surface integral |/ F · dS, where F = yi – rj + zk and S is the part of the sphere 1² + y? + 2? = 4 in the first octant with inward orientation.
Scalar Surface Integral. A scalar surface integral is I| (7, y, =) dS = ||, s (r(u, v)) ||r. x ro|| du dv where f is a scalar function defined on the parametric surface r(u, v). 1. Evaluate the surface integral where S is the part of the plane r+ y + 2z = 2 in the first octant. Vector Surface Integral (Flux Integral). Suppose F is a continuous vector field on an oriented surface S with unit normal vector n. The surface integral of F over S is F. dS = = || F· (r„ × r,) du dv F.ndS 2. Evaluate the surface integral |/ F · dS, where F = yi – rj + zk and S is the part of the sphere 1² + y? + 2? = 4 in the first octant with inward orientation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Scalar Surface Integral. A scalar surface integral is
f(2, y. 2) dS = ||, s (r(u, v)) ||ru × r,|| du dv
where f is a scalar function defined on the parametric surface r(u, v).
1. Evaluate the surface integral
'SP (= + 1)//
where S is the part of the plane r + y + 2z = 2 in the first octant.
Vector Surface Integral (Flux Integral). Suppose F is a continuous vector field on an oriented
surface S with unit normal vector n. The surface integral of F over S is
F. dS
F.:
·n dS
F. (r, x r,) du dv
2. Evaluate the surface integral /| F
dS, where F = yi – xj + zk and S is the part of the sphere
a² + y? + 2? = 4 in the first octant with inward orientation.
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