of the region enclosed by さ2:三mxとュ- Sec'x-1 Q Find the anea from x~0 ×-Thく to (Brange Color)

Q: Evaluate the Integral iF the funthun X = = XSin (xy) ニ over the vecfongulor region R- [0,1][1, 2]

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Q: Compute the Cauchy principal value of the following integral using residue theory details): 2+1 dz…

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Q: 5. Use the binomial expansion and Cauchy's Integral Theorem to evaluate ( с 2n dz Z + -/-/-) where C…

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Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: Verify the Divergence theorem over a cube in one unit on each side. The cube is situated in the…

A: By, Divergence theorem we have, The cartesian system for the first octant is,

Q: Calculate the area of the inner loop of r = √3 − 2 cos θ.

A: To Find: Area of the inner loop of r.

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

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Q: Calculate Hhe fourier coeffrecents Of the fancdion fR) over the nderval -スと×L2 here: Fx)=(0,-2くメCー…

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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: Compute ffs FdS for F = where S surface of the olid region bounded on the "side" by the cylinder x²…

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Q: Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices…

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Q: 3)Evaluate /y² + 1dA , Ris bounded by x = 4 - y² ,x = 0 R

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Q: Obtain the moment of the area generated by x = 2a, bounded by x =y and x2 = 2av.

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

A: detailed solution is given below

Q: Evaluate the integral (ycoS z + 1) dydz.

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Q: 2. Evaluate S SR 72xydA by making appropriate change of variables, where R is the region bounded by…

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Q: Find the differential cquation a the (2.K) families af cirdes with center at and wi th radius r

A: To find: Differential equation of circle with centre 2,k and radius r. We know that equation of…

Q: and let ah -(-1'I Let In tan (a) for n = 0,1, 2 Intz 1) Show that In + Io+ り+! (-1)" for nal an-…

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Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: . Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj…

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Q: Evaluate the integral Sdx using the two-point Gaussian quadrature rule 1+z² -2 2444 O O OOO N|WO…

A: We have to evaluate the integral ∫−2221+x2dx using the two-point Gaussian quadrature rule. Here,…

Q: To integrate by u-substitution, which part of the integrand should you choose as u? SG) · 2ª · In 2…

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Q: In?(In(ar)) dr. a >0 -dx, a > 0 а. 2.x In(ax)

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

A: I have Provided this answer in step-2.

Q: egral dS over the su 9, where n is th surface element

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Q: Evaluate the integral S 3012 2/3 de using the two-point Gaussian quadrature rule. 1+16z4

A: Given integral is ∫−121221+16x4dx. We have to evaluate the given integral by using the two-point…

Q: Evaluate the given integral where C is the directed line segment that joins the point 1 to the point…

A: The given problem is to evaluate the given path integral over given path of line segment joining…

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

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Q: 4. Evaluate the iterated integral: dydx. 1/4 Ja2

A: The solution are next

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

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Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: 3. Evaluate JIJ 62² dV where G is bounded by x + 2y + 4z = 8 in the first octant.

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Q: compute J secx dr. I n trying to integrate

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Q: Is Ź U Ź,asigma a lgebra over X? 4. Prove your an swer.

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Q: Sketch the region which is defined by the given condtions. 0 ≤ θ ≤ π, r ≤ 3

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Q: Let D be the solid region in space bounded below by p = -- and above by cosp p = . Then the region D…

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: calculate improper integral Poorreligggms ecosemberererii wemer- J $in I + CO8IC Vsinx - CasI paul:

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Q: Find the solid of revolution that results when the region under the graph of f(x) = xvsin x for 0< x…

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Q: 10- For the shaded area shown in fig. Determine the coordinate of the centroid

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Q: = Compute the area of the region bounded by y hyperbolic or inverse hyperbolic functions. 1 √x²+16…

A: We compute the area of the region bounded by y=1/√(x2+16) over the interval [ 0,3 ] hyperbolic or…

Q: xplain why the annulus {z: 1 |Z| 2} is not simply connected.

A: By using Cauchy's theorem G is not simply connected.

Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Q: use the funda men tal Theorem of Culculus to find the under Curue of 2. y = -xFl0 x between x = 3…

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Q: D Find a singular saluhion of DE: %3D

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Q: *Sketch all appropriate regions or solids." Evaluate the integral [[2y² cos(xy) dydx.

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