of Jelution Discuss passibility of existence ux)= Sinfox +257 K(1,)u() dt %3D Sn(t+ /4) Sin (x-E); %3D Find the Selution Ĥ exists.

Q: a) Find the area between the curve Y = sinx and the x-axis on the interval [0, 37] in the figure 1.…

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Q: 1 e-r/2 dx = 1. (2m

A: Using double integral of Cartesian form and polar form.

Q: (0) ) Eva luale Ihe follo wing de fini le integol by using Ihé properties of Beta and Gomma…

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Q: dx V4-x² O -V4 – x² + c O - In v4 – x² + c O sin +c -1 x 2 O 2v4 – x2 + c

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Q: (b) Find the Fourier cosine and sine integrals of f (x) = e¬kx, for x > 0, k > 0. %3D

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Q: 8o lve uaing beta gamma funchon m-1 h-1 dx dy from Me beta funchien formula & elalion X vaies o o1-Y…

A: Given integral is  I=∫01∫01-yxm-1yn-1xydxdy            (i) Now,…

Q: y® cos(3y) dy

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Q: 1. S (5x-12) dx 2. S x³-6x² +8x 3. S -(3 cos² 0 +8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0 dx…

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Q: 4. dx J x Inx VInx2 -1 A C - sec-1 (In xx) + C sec-1 - In x sec-1 (In x) + C + C In x. sec-1 O A В E…

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: ull Pure Talk 12:55 PM 90% s3.us-east-1.amazonaws.com 1 | w(w2 + 1)³dw -1 x3 1 dx x2 sin30cos0 d0…

A: ∫-11ww2+13 dw=0, Since ww2+13 is odd.

Q: 10 - f sin(82) arctan(sin 4x) da integralinin değeri aşağıdakilerden hangisidir? a) O T-2 b) - 8 8(T…

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Q: 3. dy - 2** + e 2x cos (x) + Cos(x) y Fuctor8 Integrating

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Q: ution 1- u? cos x and dx 1+ u? grand to a rational function of u, and t al. If you have a CAS, use…

A: We have to find the indefinite integral according to the given information

Q: Test for exactness (2ysinxcosx - y + 2y?ey )dx = (x - sin?x - 4xye*y )dy %3D solve exact de,…

A: First we have to check exactness then we solve the differential equation.

Q: 1. a) For 0<x<1, show that /2 1+ x b) Use the estimate in a) and integrate it to prove that 1 1 -dx…

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Q: 17. When we use the integration by parts to integrate * sin-x dx we obtain an expression of the form…

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Q: 20) Using integration by parts, if J cos(Inx)dx = uv + J sin(ln x)dx, what is uv? A. cos(In x) B.…

A: According to our guidelines, we can only provide a solution to one problem at a time. You can always…

Q: sin-1x If y = dy cos(t) dt, then dx Select one: a. cos(sin-1x) b. X /1-x² c. Non of them d. 1 e. 1…

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Q: (a) Find the MacLaurin polynomial of degree 9 for the function h(x) = ln(1 + x3). (b) Use you answer…

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Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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Q: (a) Use the Trapezoidal Rule, with n = 5, to approximate the integral f 6 cos(4x)dx. T5 (b) The…

A: According to our guidelines , we can answer only first three sub-parts. Kindly re-post other…

Q: aw Find for w e" sin p where ax p = sin x q = z2 In y x- at (x,y,z)3글) %3D z2 e sin-1 x = Hint: dx…

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. A cosx siny = c B sinx cosy…

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Q: 13. S /(1– cos x)dx

A: Follow the procedure given below.

Q: Sheet 5 Numerical analysis QI/ Evaluate f (x² + 3y?) dy dx using Simpson's 1/3 rule in x-axis and…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: dx 3. Evaluate: S V(x+2)(3-x) A. sin-1 (*) + 3x- C.V6 +x – x² -In |x-+v6 + x – x² |+C B. sin-1 (*)-…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: y2) = Br* -cos x. %3D A. 24x2 B. 24x + sin x+2 Given h(x) = -sec²x, determine the general…

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Q: ( 3cos x - 1 1- sin?x To evaluate dx the integrand can be transformed to o f(3tan?x - csc?x)dx 3cosx…

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Q: e2x Evaluate the integral: dx 1 + eX

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Q: The coefficient of sin(x) in the antiderivative of F(x) =| cos 2 %3D

A: Given: F(x)=cosx26

Q: a) Find the indefinite integral of the function 1 y = 3t2 + 2e3t +- + 2 cos 3t | b) Calculate the…

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Q: (4) Given that Firsy)= (y- E cos ) +(2xy +e sind) S is Conservative IR on (a) Find a Potential for F…

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Q: Question 16 Consider parts? A B -S₁²x sinx dx. Using integration by parts, let u = e2x, dv = sinx…

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Q: Q2 Show that the region included between the cardioids r=a (1+ cos 0) r = a (1- cos 0) is given by:…

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Q: 1. S(tan -1)ʻ dp 2. sin2 B cos B dB .5 xdx 3. S (-7-8x-x* 4. Sx³ (a2 + x2) dx xdx 5. f (x²+a²)³ 6.…

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Q: 16) Approximate ,xer'dx Using Gauss-Legendre 3 points formula G3(f)

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Q: II. Definite Integral 1. V2 dx V3-1 x2/4-x2 ans: 4 jž sim 16 2. S7 sin*xcos7xdx ans: 1155

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Q: y In sin-1 e y' = A - On 4 – In z) sin- (G) A )I 4 – x² IT x-1 1 ® y' = x sin-1 V4 – x2 -

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Q: A. Bernoulli 's Equation e-2x 3 1. yl =y- xy°c %3D | 2. ( 3 tan X 2 cos y) sto xdx t tan xsin ydy -…

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Q: Question 008: Complete the following question involving Integratin by Parts Method. Given the…

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Q: sinh (z) = %3D e -e 2- e?+ez e2+ez 21 eiz +e-iz 2.

A: We need to find the value of the function sinh(z) Four options are given. So the solution to the…

Q: Q3/ Solue The Following Simul taneous equatron -y + Sin t + Cost %3D dt where x (6) = 1 ,x') =0,…

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Q: II. Test for exactness. If it exact, solve. 1. (x- 2y)dx – (2x + 5y)dy = 0 2. (4x³y-18x² + y)dx+ (x*…

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Q: 01 (test for exactness) * 4 points (siny - ysinx) dx +(cosx +xcosy) dy =0 01 (solve exact de) * 4…

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Q: EXAMPLE 3 Find the area under one arch of the cycloid x = r(0 – sin(0)) y = r(1 – cos(0))

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Q: 10 - S sin(8a) arctan(sin 4x)da integralinin değeri aşağıdakilerden hangisidir? 9118002 8(T – 2) a)…

A: Given that  The integral  To evaluate the integral

Q: + oo Consider the improper integral dx . What will be an appropriate solution and answer? x2+ 2x+ 2…

A: We have to find solution of improper integral.