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Evaluate the line integral J Vo• dr for the following function p and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. 2 P(x,y,z) = x? +y? +z? 2 x +y +z 3n C: r(t) = (cos t, sin t, for - sts 2 2 6 ..... (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 3n 2 dt (Type exact answers.) 2 6 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) O A. IfA is the first point on the curve, ( ), then the value of the line integral is p(A). O B. If B is the last point on the curve, ( ), then the value of the line integral is p(B). O C. If A is the first point on the curve, ( ), and B is the last point on the curve, P(A) – p(B). I) then the value of the line integral is D. If A is the first point on the curve, (ULD, and B is the last point on the curve, OD, then the value of the line integral is P(B) – p(A).

Evaluate the line integral J Vo• dr for the following function p and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. 2 P(x,y,z) = x? +y? +z? 2 x +y +z 3n C: r(t) = (cos t, sin t, for - sts 2 2 6 ..... (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 3n 2 dt (Type exact answers.) 2 6 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) O A. IfA is the first point on the curve, ( ), then the value of the line integral is p(A). O B. If B is the last point on the curve, ( ), then the value of the line integral is p(B). O C. If A is the first point on the curve, ( ), and B is the last point on the curve, P(A) – p(B). I) then the value of the line integral is D. If A is the first point on the curve, (ULD, and B is the last point on the curve, OD, then the value of the line integral is P(B) – p(A).

Calculus: Early Transcendentals
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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Evaluate the line integral J Vo• dr for the following function p and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. 2 P(x,y,z) = x? +y? +z? 2 x +y +z 3n C: r(t) = (cos t, sin t, for - sts 2 2 6 ..... (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 3n 2 dt (Type exact answers.) 2 6 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) O A. IfA is the first point on the curve, ( ), then the value of the line integral is p(A). O B. If B is the last point on the curve, ( ), then the value of the line integral is p(B). O C. If A is the first point on the curve, ( ), and B is the last point on the curve, P(A) – p(B). I) then the value of the line integral is D. If A is the first point on the curve, (ULD, and B is the last point on the curve, OD, then the value of the line integral is P(B) – p(A).
Transcribed Image Text:Evaluate the line integral J Vo• dr for the following function p and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. 2 P(x,y,z) = x? +y? +z? 2 x +y +z 3n C: r(t) = (cos t, sin t, for - sts 2 2 6 ..... (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 3n 2 dt (Type exact answers.) 2 6 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) O A. IfA is the first point on the curve, ( ), then the value of the line integral is p(A). O B. If B is the last point on the curve, ( ), then the value of the line integral is p(B). O C. If A is the first point on the curve, ( ), and B is the last point on the curve, P(A) – p(B). I) then the value of the line integral is D. If A is the first point on the curve, (ULD, and B is the last point on the curve, OD, then the value of the line integral is P(B) – p(A).
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