Evaluate the line integral 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. P(x,y) = 2x + 4y; C: r(t) = (2 – t,t), for 0sts2 (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. J (2) dt (Type exact answers.) (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed.) 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. IfA is the first point on the curve, and B is the last point on the curve, , then the value of the line integral is P(A) – p(B). D. If A is the first point on the curve, (2,0) , and B is the last point on the curve, (0,2), then the value of the line integral is p(B) – P(A). Using either method, J vo• dr = 4. (Type an exact answer.)
Evaluate the line integral 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. P(x,y) = 2x + 4y; C: r(t) = (2 – t,t), for 0sts2 (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. J (2) dt (Type exact answers.) (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed.) 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. IfA is the first point on the curve, and B is the last point on the curve, , then the value of the line integral is P(A) – p(B). D. If A is the first point on the curve, (2,0) , and B is the last point on the curve, (0,2), then the value of the line integral is p(B) – P(A). Using either method, J vo• dr = 4. (Type an exact answer.)
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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Transcribed Image Text:Evaluate the line integral J Vq• 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.
P(x,y) = 2x + 4y;
C: r(t) = (2 - t,t), for 0sts2
.....
(a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration.
2
J (2) dt (Type exact answers.)
(b) Select the correct choice below and fill in the answer box(es) to complete your choice.
(Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed.)
O A. If A 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,
then the value of the line integral is p(A) - p(B).
O D. If A is the first point on the curve, (2,0) , and B is the last point on the curve, (0,2) , then the value of the line integral is P(B) - P(A).
Using either method,
C
Į V@• dr = 4.
(Type an exact answer.)
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