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7) Let F = <-y^2, x, z^2>. Let C be the curve parameterized by r(t) = <cos t, sin t, 0>, 0 <= t <= 2pi. a) Compute int_C F . dr b) Evaluate int_C F . dr by using Stokes' Theorem where S is the top of the sphere x^2 + y^2 + z^2 = 1. c) Evaluate int_C F . dr by using Stokes' Theorem where S is z = 1 - x^2 - y^2.

          7) Let F = <-y^2, x, z^2>.
Let C be the curve parameterized by r(t) = <cos t, sin t, 0>, 0 <= t <= 2pi.
a) Compute int_C F . dr
b) Evaluate int_C F . dr by using Stokes' Theorem where S is the top of the sphere x^2 + y^2 + z^2 = 1.
c) Evaluate int_C F . dr by using Stokes' Theorem where S is z = 1 - x^2 - y^2.

7) Let F = <-y^2, x, z^2>.
Let C be the curve parameterized by r(t) = <cos t, sin t, 0>, 0 <= t <= 2pi.
a) Compute intC F . dr
b) Evaluate intC F . dr by using Stokes' Theorem where S is the top of the sphere x^2 + y^2 + z^2 = 1.
c) Evaluate intC F . dr by using Stokes' Theorem where S is z = 1 - x^2 - y^2.

Added by Heather K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/11/2023

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F = <-y^2, x, z^2>. Let C be the curve parameterized by r(t) = <cos t, sin t, 0>, 0 <= t <= 2pi. a) Compute int_C F * dr b) Evaluate int_C F * dr by using Stokes' Theorem where S is the top of the sphere x^2 + y^2 + z^2 = 1. c) Evaluate int_C F * dr by using Stokes' Theorem where S is z = 1 - x^2 - y^2.