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1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) : -2+2t +t = -2+3せ) yle)= (1-と)(-1)+t(2) |tt + 2t = 「-1t 3と x(と)- 3 oとtと1 yは)= 3 %3D

1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) : -2+2t +t = -2+3せ) yle)= (1-と)(-1)+t(2) |tt + 2t = 「-1t 3と x(と)- 3 oとtと1 yは)= 3 %3D

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 21E
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Would someone please double check my work for problem 1. Please and thank you!
1. Evaluate 4x³ds, where Cis the line segment trom F2,-1,Q T,4). x' (t) = 3 y'(t) = 3 +e(6), y(e))= (-143€)(-14らも): 2- it-3t+1ピ X(+)= -2+3t x(E) = (1-t)(-2) + t(1) UE) = -2+2t +t = -2+3€) yle) = (1-t)(-1) +t(2) y(E) = -1+t + 2t = [-1+ 3t ylt) = -1+3t = 94? -9t + 2 %3D + 2t =2.12132034356 2. Find the value of f, xy dx + Jy² + 1dy, where C is the path shown on the graph (6x-Pu) dA elo (Hpt: Upe Cjeen s the orer.} で 5. Green's Theol boundary curve C that is a piecewi counterclockwise. Let F = <P, Q> E continuous partial derivatives on D fF.dr = 6 · dr : Green's Theorem, Flux Form: Le curve C that is a piecewise smoot counterclockwise. Let F = <P, Q> continuous partial derivatives on a the region betwveen If F = <P, Q> is a vector field and defined by: If F = <P, Q> is a vector field and Bri) drde If the net rotation is counterclock then it will be negative. 972-(-A68.75) do 3162.0130016)
Transcribed Image Text:1. Evaluate 4x³ds, where Cis the line segment trom F2,-1,Q T,4). x' (t) = 3 y'(t) = 3 +e(6), y(e))= (-143€)(-14らも): 2- it-3t+1ピ X(+)= -2+3t x(E) = (1-t)(-2) + t(1) UE) = -2+2t +t = -2+3€) yle) = (1-t)(-1) +t(2) y(E) = -1+t + 2t = [-1+ 3t ylt) = -1+3t = 94? -9t + 2 %3D + 2t =2.12132034356 2. Find the value of f, xy dx + Jy² + 1dy, where C is the path shown on the graph (6x-Pu) dA elo (Hpt: Upe Cjeen s the orer.} で 5. Green's Theol boundary curve C that is a piecewi counterclockwise. Let F = <P, Q> E continuous partial derivatives on D fF.dr = 6 · dr : Green's Theorem, Flux Form: Le curve C that is a piecewise smoot counterclockwise. Let F = <P, Q> continuous partial derivatives on a the region betwveen If F = <P, Q> is a vector field and defined by: If F = <P, Q> is a vector field and Bri) drde If the net rotation is counterclock then it will be negative. 972-(-A68.75) do 3162.0130016)
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