Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Let y be the part of the curve y = x? running from (-1, 1) to (2,4). Calculate
xy dx + (x + y) dy.
2. Let E be the piece of the cone z =
Vx2 + y? lying between z = 0 and z = 1, oriented with the
'outward' (pointing away from the z-axis) normal. Let F be the vector field given by F(x, Y, z) =
(xy, 0, –z). Compute the flux
F. dA.
Σ
3. Let E be the part of the unit sphere x2 + y? + z2
= 1 where z > Vx² + y?. Calculate
22 dA.
Transcribed Image Text:1. Let y be the part of the curve y = x? running from (-1, 1) to (2,4). Calculate xy dx + (x + y) dy. 2. Let E be the piece of the cone z = Vx2 + y? lying between z = 0 and z = 1, oriented with the 'outward' (pointing away from the z-axis) normal. Let F be the vector field given by F(x, Y, z) = (xy, 0, –z). Compute the flux F. dA. Σ 3. Let E be the part of the unit sphere x2 + y? + z2 = 1 where z > Vx² + y?. Calculate 22 dA.
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