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Consider ∫ ( cos x ) 3 ( sin x ) 2 d x . The appropriate integration technique is C .A) u -substitution with u = ( cos x ) 3 . B) Integration by-parts with u = ( cos x ) 3 and d v = ( sin x ) d x . C) u -substitution with u = sin ( x ) . D) u -substitution with u = cos ( x ) . E) Integration by-parts with u = sin ( x ) and d v = ( cos x ) 3 d x . The expression that is equivalent to ∫ ( cos x ) 3 ( sin x ) 2 d x is V) .I) − ( cos x ) 4 − 3 ∫ ( cos x ) 3 sin x d x II) − 3 ( sin x ) 2 ( cos x ) 2 + 3 ∫ ( cos x ) 3 sin x d x III) − ∫ u 3 d u IV) ∫ ( u 2 − u 4 ) d u V) ∫ ( u 3 − u 5 ) d u
Which of the follow is an appropriate technique to evaluate the integral ∫xcos(3x)dx?A) Use u-substitution with u = x . B)Use u-substitution with u = cos ( 3 x ) . C) Use Integration-by-Parts with u = x and d v = cos ( 3 x ) d x . D) Use Integration-by-Parts with u = 3 x and d v = x d x . E)
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 -...
41&43 In Problems 41-46, use the given information and appropriate identities to find the exact value of the indicated expression. 41. Find sin(x + y) if sin x = 1/3, cos y = -3/4, x is in quadrant II, and y is in quadrant III. 42. Find sin(x - y) if sin x = -2/5, sin y = 2/3, x is in quadrant IV, and y is in quadrant I. 43. Find cos(x - y) if tan x = -1/4,...
III. Consider the series connections 4. Consider the series connections of the canacitors shown below: (0) - (1) (0) C+ 01 ✓ C+,(0) A. If G =2uF, =3uF and C=6uF a) Find the equivalent capacitance of the series combinations C.Cand C b) Give the expression relating it) and v) c) If y = 2V, v = 4V and v=1V, determine the energy stored in each of the capacito .Cand B. If the voltage v(()=sin ox and C=luf compute the following...
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))...
HELLO I AM CURRENTLY IN DIFFERENTIAL EQUATIONS PLEASE EXPLAIN EACH STEP SO I CAN LEARN FROM YOU (I KNOW SOME PEOPLE ONLY CARE ABOUT TEH ANSWER, BUT WILL REALLY APPRECIATE IT) TO SAVE TIME FEEL FREE TO JUST SAY A LAW, THEOREM, OR CONCEPT FOR AN EXPLANATION AND I CAN GO AHEAD AND STUDY IT ON MY OWN. i REALLY DO READ THESE VERY CAREFULLY AND USE THE COMMENTS OFTEN, SO JUST A LITTLE HEADS UP. I FIND IT DIFFICULT...
PLEASE ANSWER ALL NUMBER 3 (Parts A-F) Consider the following list of properties 3. f(x)oo x-+1 ii) lim()2 iv) f(1)-3 v) lim f(x)-n x+1 For each of the following, decide if it is possible for a function to have the given set of properties. If so, sketch and label a possible graph for the function on the axis provided. If no such function is possible, explain why not. a) (i) and (i) b) (), (ii), and (iv) c) (i), (iii),...
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...