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Evaluate the line integral Vo• dr for the following function op and oriented curve C (a) using a C parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. x² + y² +z² 2 p(x,y,z)= C: r(t)= (cos t, sint, ). T for 7 sts 5π 4

Evaluate the line integral Vo• dr for the following function op and oriented curve C (a) using a C parametric description of C and evaluating the integral directly, and (b) using the Fundamental Theorem for line integrals. x² + y² +z² 2 p(x,y,z)= C: r(t)= (cos t, sint, ). T for 7 sts 5π 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate the line integral Vop.dr for the following function 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. x² + y² + z² 2 5п 4 T 4 p(x,y,z) = 5T C: r(t) = (cost, sint.). forsts 5 4 sint cost + sint cost + t T *** dt (Type exact answers.) (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) OA. 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(B) - (A). OB. 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) - (B). OC. If B is the last point on the curve, (..), then the value of the line integral is (B). OD. If A is the first point on the curve, (), then the value of the line integral is q(A).
Transcribed Image Text:Evaluate the line integral Vop.dr for the following function 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. x² + y² + z² 2 5п 4 T 4 p(x,y,z) = 5T C: r(t) = (cost, sint.). forsts 5 4 sint cost + sint cost + t T *** dt (Type exact answers.) (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) OA. 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(B) - (A). OB. 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) - (B). OC. If B is the last point on the curve, (..), then the value of the line integral is (B). OD. If A is the first point on the curve, (), then the value of the line integral is q(A).
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