Question

Please explain as you solve, thank you! (#1,2 & 4)

an arbillal equation is continuous il nu xo would, for small enough pos This establishes Equation 3. EXERCISES In Exercises 1 to 4, use Green's theorem to compute the value of the line integral y dx + xédy, where y is the indicated closed path. 1. The circle given by g(t) = (cost, sin t), 0 < t < 211 2. The square with corners at (+1, 1), traced counterclock- wise 3. The square with corners at (0, 0), (1, 0), (1, 1), and (0, 1), traced counterclockwise 4. The ellipse x2 + 4y2 = 4, traced clockwise 5. Use each of the three paths 71, 72, or y3 in Example 3 of the text to compute this path-independent line integral from (0,0) to (1,1): y dx + x dy. Jy 6. Let y be the curve parametrized by g(t) = (2 cost, 3 sint), Osts 2n. Compute (2x + y) dx + (x + 3y) dy. Jy In Exercises 7 to 10, evaluate the following line integrals by whatever method seems simplest.

Answer 1

Y=sint ust de-simb dt dy t dt + A Lint (sintJdt urt Crsb dt ers dt st 1-nrt dt eEst-Lit dnt d -7 -7 (Aw) A (1) 2. A to B Fm d - (- (V-) - 2 1 D, - to m d 0 1. dy= 2 dn rom D to A, - -L+1)-2) +2-4 (A)

4. +. 255 t 0ts2 Y cimt sint (-2int) dt cloekwic 4esrt u dt EC 2sintt t 4 urs ess24- 4(1-sintt) ust + CAn) 1 Ap 9789 i