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A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 6. (The fractional residue theorem) Show that sin(ar) L r(r² + 1) tz = 5(1 – e~“), a>0. iaz [Hint:…

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Q: Consider the integral below 4 dr. 1+x²° (a) Approximate the integral using Gaussian quadrature with…

A: Given integral is I=∫0141+x2dx we have  f(x)=41+x2 By Gauss quadrature with 2 points, let the…

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Q: 2 ecos cos(send) 0 5-4 cos(6) Jo -do = 2π € 500 cos cos(sen)

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Q: 5) Evaluate the integral.cusc c for the constan6 of integrafion) 2(ean cx) +6an cx>) dx

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

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Q: 8. What domain D in space minimizes the value of the integral // (4x² + y^ + z2² – 4)dV

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Q: Consider the following. Ju-(5 - u? + u°) du Simplify the integrand by distributing u3 to each term.…

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Q: * Use the Grom Schmidt process for thi two_ dmensional space: 2 3. 4 2

A: Gram Schmidt process is given by: uk→=vk→−∑j=1k−1uj→⋅vk→|uj→|uj→   v1→=201, v2→=3-51, v3→=042,…

Q: İki noktalı Gauss kareleme yöntemini kullanarak S dx integraline 1+16x4 yaklaşık değer bulunuz. 2…

A: we have given by integral ∫-12128x21+16x4dx we have to solve the integral by using two-point…

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Q: In Exercises 15–22, graph the integrands and use known area formu- las to evaluate the integrals.…

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Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

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Q: What is the integrable form of dr? ex – e -* e u²) 2 du 2 du du

A: We have to find the integral

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Q: 15. Evaluate the integral zVx² + y²dzdxdy by using cylindirical coordinates.

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Q: Evaluate the double integral || 8xy dA, where D is the triangular region with vertices (0, 0), (1,…

A: Given data: The first vertex is O=(0, 0). The second vertex is B=(1, 2). The third vertex is A=(0,…

Q: a) Find the triple integral xdV.

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Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

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A: Topic:- limit and continuity

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Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

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Q: Evaluate the double integral || 8xydA, where Dis the triangular region with vertices (0,0), (1,2),…

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Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

Q: İki noktalı Gauss kareleme yöntemini kullanarak da integraline yaklaşık değer bulunuz. Evaluate the…

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Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

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Q: to find the aren ruse 2) Use a polar integral enclosed by the three-petaled r = singe

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Q: İki noktalı Gauss kareleme yöntemini kullanarak 2 8x? -dx integraline yaklaşık değer bulunuz. 1+16x4…

A: We have to Evaluate the integral ∫-12128x21+16x4dx by using two-point Gaussian quadrature rule. As…

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Q: What is the integrable form of dr? 1 -1) du -u?) 2 du 2022-01..

A: Find the integrable form by substitution method

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Q: In Exercises 11-59, evaluate the integral using the appropriate methodor combination of methods…

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