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Figure 5.16 Level curves of Exercise Figure 5.15 Level curves of Exercise I. 2. The level curves of a function f(x, y) are concentric circles centered at the ongn, e Figure 5.16. Compute the path integral of f(x. y) along (a) The semicircle x+y=4,y0 (b) Quarter-circle x+y9, xs0ys0 Exercises 3 to 1l: Compute fds. 3. f(x.y) 2xr-y, et) (e'+1, e'-2), 0st s m 2 4. f(x, y.2)=xy, et) (2 cos t, 3 sin r, St), 0s ts*/2 5. fix, y, 2) (x+y+), ee) (t,t, t), I

Figure 5.16 Level curves of Exercise Figure 5.15 Level curves of Exercise I. 2. The level curves of a function f(x, y) are concentric circles centered at the ongn, e Figure 5.16. Compute the path integral of f(x. y) along (a) The semicircle x+y=4,y0 (b) Quarter-circle x+y9, xs0ys0 Exercises 3 to 1l: Compute fds. 3. f(x.y) 2xr-y, et) (e'+1, e'-2), 0st s m 2 4. f(x, y.2)=xy, et) (2 cos t, 3 sin r, St), 0s ts*/2 5. fix, y, 2) (x+y+), ee) (t,t, t), I

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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Figure 5.16 Level curves of Exercise Figure 5.15 Level curves of Exercise I. 2. The level curves of a function f(x, y) are concentric circles centered at the ongn, e Figure 5.16. Compute the path integral of f(x. y) along (a) The semicircle x+y=4,y0 (b) Quarter-circle x+y9, xs0ys0 Exercises 3 to 1l: Compute fds. 3. f(x.y) 2xr-y, et) (e'+1, e'-2), 0st s m 2 4. f(x, y.2)=xy, et) (2 cos t, 3 sin r, St), 0s ts*/2 5. fix, y, 2) (x+y+), ee) (t,t, t), I<t< (Hint: Take Istshahe on pute the limit as b approaches o) 6. f(x, y) x'+y, e is the part of the curve x3+ l in the first quadrant 7. f(x, y. 2)= y-, et) i+ Inj+2rk, 1 sts4 8. f(x, y) x+ 3y-xy, e is the circular are of radius 3 in the xy-plane, from (3)(-3 9. f(x, y, 2) xyz, e is the helix given by et) (2 sin t, 4t, 2 cos t), 0sIsor 10. f(x, y, 2)= (x+y+/x+ y+) e is the straight-line segnent joining ( (a, a, a), where a 1 11. f(x, y) e, e is the line segment in R fhom (0, 0) to (3,-4) 12. Compute ds, where f(x, y, 2) x+2y- and e consists of the parabolic pwh f from (0, 0, 0) to (1, 1,0), followed by the straight line to (1,-1,). 13. Compute ds,where f(x, y, 2) x-4y+2. andeconsists of the straight line fiom(&20 to (0, 2, 0), followed by the circular path in the yz-plane (and above the xy plane) with is as the origin, from (0, 2, 0) to (0,-2, 0).
Transcribed Image Text:Figure 5.16 Level curves of Exercise Figure 5.15 Level curves of Exercise I. 2. The level curves of a function f(x, y) are concentric circles centered at the ongn, e Figure 5.16. Compute the path integral of f(x. y) along (a) The semicircle x+y=4,y0 (b) Quarter-circle x+y9, xs0ys0 Exercises 3 to 1l: Compute fds. 3. f(x.y) 2xr-y, et) (e'+1, e'-2), 0st s m 2 4. f(x, y.2)=xy, et) (2 cos t, 3 sin r, St), 0s ts*/2 5. fix, y, 2) (x+y+), ee) (t,t, t), I<t< (Hint: Take Istshahe on pute the limit as b approaches o) 6. f(x, y) x'+y, e is the part of the curve x3+ l in the first quadrant 7. f(x, y. 2)= y-, et) i+ Inj+2rk, 1 sts4 8. f(x, y) x+ 3y-xy, e is the circular are of radius 3 in the xy-plane, from (3)(-3 9. f(x, y, 2) xyz, e is the helix given by et) (2 sin t, 4t, 2 cos t), 0sIsor 10. f(x, y, 2)= (x+y+/x+ y+) e is the straight-line segnent joining ( (a, a, a), where a 1 11. f(x, y) e, e is the line segment in R fhom (0, 0) to (3,-4) 12. Compute ds, where f(x, y, 2) x+2y- and e consists of the parabolic pwh f from (0, 0, 0) to (1, 1,0), followed by the straight line to (1,-1,). 13. Compute ds,where f(x, y, 2) x-4y+2. andeconsists of the straight line fiom(&20 to (0, 2, 0), followed by the circular path in the yz-plane (and above the xy plane) with is as the origin, from (0, 2, 0) to (0,-2, 0).
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