2 6 Ine 1 Question 7 1 pts Which of the following integrals is equivalent to...
Indefinite integrals. Use table 5.6 or a change of variables to evaluate the following indefinite integrals. check your work by differentiating. 2. 1 dx, x 2 32 xV4x2-I Table 5.6 General Integration Formulas cos ax C a sin ax C 1. cos ax dx = 2. sin ax dr se' 3. 4. ax dx=- ax dx -tan ax C a cot ax C 1 sec ax tan ax dx=-sec ax C 1 --csc ax C csc ax cot ax 5....
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 13 Consider the iftegral 22 -dz V1 + 23 Which of the following integrals is equivalent to this under the substitution u = 1 + 23? u2 du V1+23 Ta s rudu (x - 1) du Set 3 du yu 1 du yu
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
which of the following integrals equals: Question: Which of the following integrals equals lim n-00 2n of cos(2²) de of costa", de o lo confort de None of the above LA RUS
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...
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
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
9) (6 pts) Indicate which of the following integrals would evaluate to be zero (There could be many). You should be able to do this by inspection. a) S5172 t sin (3w.t) dt b) =112 sin (3w.t)sin (3w.t) dt c) (172 sin (3w.t)cos (5w.t) dt CT/2 cos (7w.t)cos (5w.t) dt e) Le-jwt etjwt dt f) Lee-jwt e-jwt dt