QUESTION 1 Compute [[ ev** where Q is bounded by y = V100-x-z AP 2++ and y = 0.

Q: 7. Let S = [0, 1] × [0, 1] and ƒ: S → R be defined by f(x, y) (2x³+y², 10, Show that f is integrable…

A: Follow the steps.

Q: Theorem 6. Let X, Y be jointly continuous random variables. Then E[Y] = | E[Y|X = x] fx(x) dx %3D…

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Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian. b. Establish…

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Q: The set of all values of p which makes the integral x* dx is divergent is a) (-1, 0) b) (-n,-1) c)…

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Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

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Q: Page 4of 8 3. Evaluate the following integral or show that it is divergent: roo In x xp a) S" x+1 b)…

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Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: Determine the Riemann integral partitions given by Pn = Qn = {o, 0, 1 4 1 2 4n' 4n 3+n " 6 + 2n 4n…

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Q: Verify that the integral of the beta density from −qto q equals 1 for(a) α = 2 and β = 4;(b) α = 3…

A: The Beta density function is given by: We need to prove:

Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: 4.78 Compute P(u – 20 < X < µ + 20), where X has the density function f (x) = { 6x(1 – x), 0<x< 1,…

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Q: 1 10-10z Set up the iterated double integral f S S dy dr as dxdy such that

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Q: 38. Evaluate the integral dy + x³ dx for any closed path C.

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Q: 30. Obtain the integral representation of the Neumann problem V²u = f in D, du on boundary B of D.…

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Q: Question 8 Show using e, 8 methods that the functions f (x) = 1 and g (x) = sin r %3D 1+ x2 are…

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Q: 1. (Section 17.4) Use Green's Theorem to evaluate the line integral sir sin(y) dx + x dy, where C is…

A: Use Green theorem.

Q: Evaluate the integral. e3t V2 + et dt =

A: We have to find the indefinite integral

Q: D (x) is not integrable on [0,1]

A: Note: Here we are solving 1st problem for the next problem please submit the question again. Given:…

Q: Evaluate the integral. dt V 4 + t2

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Q: Evaluate the double integral S' Sí a³y²dxdy..

A: Given that double integration and we solve it by using general property of integration. Here i…

Q: .3 Evaluate the integral LST wy+x*v+vz) dzdydx 0, 2.

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Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: 1. Sketch. the.region.cf.nbegratizon.and.evaluabe..th fallowing. integrals a. Ans. 21.In.2./2. A.. で…

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Q: Find the integral. e3t dt Vest - 3 %3D 1

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Q: Show that the following line integral is path independent (3,2) cosh (0,0) (8xdx+6ydy) 4.

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Q: (Section 17.3, 17.5) Consider F(a, y) = (e-" cos(y))i + (e-" sin(y))} (a) Show that F is…

A: Here is the solution of the given problem. Line integral:  Conservative Vector Field:

Q: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

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Q: x cos 5x dx Ste-* dt -3r

A: Solution of above question is written below.

Q: Question 9 Show that (a) f (x) = ,x E (0, ∞) and (b) h (r) = e" ,x € R, uniformly continuous on R.…

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Q: Consider the integral 2 6z² In(z) dz

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Q: Evaluate the integral. | e3t V4 + et dt = %3D

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Q: Question 3.2: Let G : z(1) =-1+÷e“, 0si< 2n and C, : z(1) =1+÷e“, 0si<2n and C: z(1) = 2e“, 0<IS27.…

A: Let the given domain isC1:zt=-1+12eit,for all 0≤t≤2πC1:zt=1+12eit,for all 0≤t≤2π andC:zt=2eit,for…

Q: The double integral over the non-rectangular region /- e dydx is equal to: None of these (e-1)/2…

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Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

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Q: fx'e* dx ets

A: To evaluate:                     ∫x2 ex3 dx

Q: is Theorem 1.6. The line integrals of f in D are independent of path if and only if f has an…

A: Given: The line integrals of f in D are independent of the path if and only if f has an…

Q: (z - 1)dt + (1 – t)dz %3D

A: (4) Given differential equation is z−1dt+1−tdz=0......1. We have to determine the whether the…

Q: 8. Evaluate the iterated integral. /8-z2-ya zdz dz dy

A: The given question can be solved as explained in step 2.

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy dA ax ду for the given path. C:…

A: This question is related to vector calculus solved in step 2.

Q: Evaluate the integral.

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Q: The maximum amplitude of the characteristic function is unity at =0, i.e, 1øx (@)| søx(0) or |øx(@)|…

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Q: Theorem 2.10 Suppose X, Y, Xn are integrable. (i) If X = a a.s., then E(X N) = a, a.s. (ii)…

A: Given X, Y, Xn are integrable

Q: What does Peano's  EU Theorem 6.1 guarantee for the IVP dy/dt = -t/y,  IC(t_o, 0)

A: Peano's theorem: Let f: Dom f→Rn be defined in a neighborhood of (t0, y0). Consider the initial…

Q: 17. Iff is bounded and integrable on [a, bl, then IfI is also bounded and integrable on [a, b] and f…

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