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Evaluate the line integral [V. dr for the following function op 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 p(x,y,z) = C: r(t)= (cos t, sint, =). 2 (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 0 J dt (Type exact answers.) * 4x forsts 3 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) A. If B is the last point on the curve.. then the value of the line integral is (p(B). B. 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)-p(A). OC. If A is the first point on the curve, (), then the value of the line integral is p(A). OD. 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). Using either method. v dr= (Type an exact answer.)

Evaluate the line integral [V. dr for the following function op 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 p(x,y,z) = C: r(t)= (cos t, sint, =). 2 (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 0 J dt (Type exact answers.) * 4x forsts 3 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) A. If B is the last point on the curve.. then the value of the line integral is (p(B). B. 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)-p(A). OC. If A is the first point on the curve, (), then the value of the line integral is p(A). OD. 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). Using either method. v dr= (Type an exact answer.)

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 [Vp. 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 p(x,y,z)= C: r(t)= (cos t, sint, dt (Type exact answers.) * 4x , forsts 3 for s 1.), (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 0 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) A. If B is the last point on the curve.. then the value of the line integral is (p(B). B. 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)-p(A). Using either method. Vp. dr = (Type an exact answer.) OC. If A is the first point on the curve, (), then the value of the line integral is p(A). OD. 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).
Transcribed Image Text:Evaluate the line integral [Vp. 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 p(x,y,z)= C: r(t)= (cos t, sint, dt (Type exact answers.) * 4x , forsts 3 for s 1.), (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use increasing limits of integration. 0 (b) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers.) A. If B is the last point on the curve.. then the value of the line integral is (p(B). B. 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)-p(A). Using either method. Vp. dr = (Type an exact answer.) OC. If A is the first point on the curve, (), then the value of the line integral is p(A). OD. 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).
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