Question 13 Consider the iftegral 22 -dz V1 + 23 Which of the following integrals is...
Question 14 Consider the integral. x(x + 5)8 dat Which of following integrals is equivalent to this integral under the substitution u = x + 5? du du ºf(wº + wº) du of 15u - v) du (e – 50%) du ºs u du
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y, z) = i + (x+yz)j + (xy – z)k and C is the boundary of the plane 2 + y + z = 4 in the first octant, oriented in the counterclockwise direction when viewed from above. the following double integrals is equivalent to this line Using Stokes' Theorem, which integral? °6964 (3 - 2z+1) du dz (2x + y) dy da Question 12...
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
2 6 Ine 1 Question 7 1 pts Which of the following integrals is equivalent to ' V1 - 22 •da 2 None of these sec (0) dᎾ tan(0) Ś tan? (0)do cos? (0) dᎾ L'ava Vudu Question 8 1 pts
QUESTION 3 Which of the following is equivalent to x/x- 2 dx if the substitution u=x-2 is used? ºs (w/2-2012) du 5'(W12-201/2) du 1 (4312 + 20 +21/2) du O plusi2 (43/2 + 2u1/2)du
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
3. Consider the triple integral 2z sin(x2 + y2 +22 - 2x) dy da dz. Set up, but do not evaluate, an equivalent triple integral with the specified integration order. a) (6 pts) da dz dy b) (7 pts) dz dr de (Cylindrical Coordinates) c) (7 pts) dp do do (Spherical Coordinates)
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
QUESTION 4 pſ3 p√3-8² √4-x² - y² Which of the following integrals is/are equivalent to soos LV***** 1 dzdy dx? rdz dr de 31 '5" 6" Secop sing dp døde IL/*** 6" 6" Sp?sino dpdo de $"p?sing dp do de 1/3 2 sec TV3 rdz dr de 1 %*%**%*-: 6" Solo branco r dz dr de
Question 5 (0.5 points) Use an integration by parts to find which of the following integrals is equivalent to In(22 - 2 + 2)dx In(x2 – 3+2)+ | J 2x2 – 3 2 - 2 + 2 zin(c? – + 2) - Sen todo xln(x2 – 2 +2)+%22277, da xln(x² – 2+2) + 2x2 – 3 1 x² – x+2