3. Compute y dV, where E is the region bounded by z = 1 -y2 - z2 and r ( E 1 Cos2 tsin2 t dt (4t - sin(4t))C 32 Hint: You might be able to make use of the fact that

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

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Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

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Q: 7. Consider the iterated integral / T * dy dz. ly=z/2 (a) Explain why we cannot antidifferentiate e…

A: Given double integral is ∫x=0x=4∫y=x2y=2ey2dydx.

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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Q: dæ, we can use integration-by-parts: udv = futo For the integral Uv – First, if we let dv e dx,…

A: Topic - integration by parts

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: 7. Evaluate the double integral S2 (x sin(y) – y sin(x)) dA over the rectangular region R= {(x, y) :…

A: We have to evaluate the double integral ∫∫Rxsiny-ysinxdA over the rectangular region…

Q: The integral ∫C[(3x2y+y2)dx+(x3+2xy)dy] is independent of the path. Evaluate the integral where C is…

A: Given: R=ti+(t2+t-2)j   for 0&lt;=t&lt;=2

Q: Evaluate the iterated integral below. π T/4 A lago S. 0 1 y cos (x) dy dx

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Q: Solve the following boundary value problem with the Galerkin method in which two equal length…

A: In the Galerkins method of approximation the trial function itself is considered as the…

Q: #6. Evaluate the line integral (y dx +z dy +x dz), where C is given by x = Vt, y = t, z = t? with…

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Q: 5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x…

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Q: -x), with respect to OY. 4. The area bounded by the curve 2x+2x -y -2 0 and the line y=2x with…

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Q: E ralu ate the given ヤyle integral: S. x² rin dy dz dx

A: Given that, The integration is, ∫0π∫0x∫0xzx2siny dy dz dx We have to find the value of this…

Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

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Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: 1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2

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Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: (a) Calculate the iterated integral 3 7/2 SS(v+y° cos x)dx dy -3 0

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Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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Q: 36 ll a O HD 57% D 8:42 2_52782976274... Evaluate:- siny dx dy SS (3-6x)dA, here Dis the region…

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Q: 2. Use the Composite Trapezoidal rule with the indicated values of n to approximate the following…

A: NOTE:Kindly repost the other question as a separate question.

Q: -1²- 5. Evaluate the integral e dV, where E is the region between two cylinders z²+z² = 4 E and 2²…

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Q: 3.33 Let D = 2pz'a, + p cos´ þa,. Evaluate (a) $D· dS (b) J,V· Ddv over the region defined by 2 < p<…

A: Given: Let D=2ρz2aρ+ρcos2ϕaz a∮SD.dS Here, We know that surface vector dS is defined as…

Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

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Q: Q1: Approximate the integral S dx with n 4 using the Simpson's rule. %3D 0 x+1

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Q: (a) Evaluate xy dA, where D is the region in R² bounded by y = sin(x) and y = = cos(x) shown in the…

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Q: 19 9% Set up the iterated double integral S S dy dæ as dxdy such that: 0 0 i. the limits of x ii.…

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Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: integrate ƒ over the given region. ƒ(s, t) = e^s ln t over the region in the first quad-rant of the…

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Q: Q2-A) Find only the limits of integration of the following: YA yA R. ty=2 ア= z dydz ( cos e sin 8)…

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 4.…

A: We have to use area formula of polar coordinates with a= pi/2 and b=2pi

Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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Q: Evaluate the iterated integral below. TL S. 1 *Sycos (x) dy dx 0

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Q: The value of the triple integral (x² + y²)dV where E is the E portion of x² + y² + z² = 4 with 0 ≤ y…

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Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

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Q: 31. Compute (x + 3y)dx dy, where D is the shaded region in Figure 16. Hint: Use the map G(u, v) = (u…

A: Given that D=6≤x+2y≤10,1≤y≤3 Let u=x+2y and v=y. Then 6≤u≤10 and 1≤v≤3. Therefore x=u-2v and y=v.…

Q: Approximate the integral fe* cos xdx using the composite Trapezoidal rule with M=5 subintervals. M-1…

A: The given integral is ∫01excos xdx. Approximate the integral ∫01excos xdx using the composite…

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem

Q: 1 dx. 10. Evaluate the improper integral m 64 + z²

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Q: 3.1. How large should n be to guarantee that the Simpson's Rule approximation to S e dx is accurate…

A: 3.1...