1. Computey yz dV, where E is the region above z = 0, below z = y, and inside r2 + y2 = 4 E

Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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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: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

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

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: Evaluate ffysin(xy)dxdy น over the region bounded by xy = 1, xy = 4, y = 1, and y = 4 using x == , y…

A: We have to find the area using double integration.

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: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Evaluate fSR f(x, y) dx dy, where R is the region given by 0<x < 2;0 < y < 5 and f(x, y) = 1 – ² –…

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Q: (b) y T= x (p) 3. Region bounded by: y = 4 – x² and y = 0. Rotate about: (a) the x-axis (с) у — —1

A: I have solved the first part for next parts repost the question

Q: 2 Evaluate 2 dA where D is the region described by 0s ys 55 - x Integral is equal to : Enter an…

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Q: 5. Evaluate z dV where E is the region bounded below by x² + y² + z² = 4 and above by x2 + y? + z² =…

A: We have to evaluate the triple integral ∭E z dV over the region E bounded above by x2+y2+z2=9 and…

Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: 2 Gwen SS8 dydx. Reverse the order √x y+8 of integration and evaluate. Draw the region. √TT (x (x²…

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Q: (iii) Sf xy²e*dA, Dis bounded by y = x,y = 2,x = 0.

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Q: s) Evaluate the triple integral, 1– y – 2) dV where E is the region given by E = {0SES y, 0<y< 4,…

A: Solution

Q: 5. Show that, in the region bounded by y = Vx and y = x2 the following double integral 3 (х + у) dA…

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Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the %3D Vr2 + y? with…

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Q: Evaluate . (y² z)dV where E be the region in the first octant E bounded by the planes x = z, x + z =…

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Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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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: 18 Evaluate EUE z(x2 +y? +z?) dV where E is the region described by 2 0szs v1-x -y

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Q: ) Evaluate Sxy dx dy R is the region bounded by x =0, x =2, y = x

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Q: Question 1. Use a change of variables to compute the integral /I. rydxdy, x3, y = 2x3, x = y³ and…

A: We have to compute the double integral ∬xydydx over the region R which is bounded by the curves…

Q: Evaluate the double integral 4 = SS R y2 dædy over the region R={(x,y)|0 < x < 4, 1 < y < 4 }

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Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

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Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

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Q: 17. (2 +y +2) dx dy dz, W is the region bounded W by x+y+z= a (where a> 0), x = 0, y= 0, and z= 0.

A: We have to solve the integral and show the graph of question 17.

Q: 21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R…

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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: (a) Evaluat e ce + arctan V)dx where C is the region bounded by y=-x,y=-1 and X = 2 %3D %3D %3D

A: Since the questions are not related so there are 6 different questions. We’ll answer the first…

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: 5. Evaluate z dV where E is the region bounded below by r2 +y² + z² = 4 and above %3D by r² + y² +…

A: We have to evaluate the integral ∭EzdV, where Eis the region bounded below by x2+y2+z2=4 and above…

Q: 13. Region bounded by: y = 4 – x and y = 0. - Rotate about: (а) the x-axis (c) y = -1 (b) у — 4 (d)…

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Q: 3. Sketch the region R defined by 0 <y < 8, ty <¤ < y!/3, then integrate dædy R

A: The region R is defined by 0≤y≤8, y4≤x≤y13the figure of R is

Q: 5) Let D be the region bounded by the curve xy 1 and the line y = = -x. Evaluate the integral xy dA…

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Q: 2. Evaluate Vye"V dA where D is the region bounded by y = x² and y = 4.

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Q: 2. Evaluate the double integral. SSp(x – 2y) dA, D = {(x, y)|1< x< 3, (1+x) < y < 2x} а.

A: As you post multiple question according to guideline I only solve the first one. Please request your…

Q: 4. Compute the value of the double integral fSRe-xydxdy, where R is the region bounded by the lines…

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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: 11.Sketch the graph of the region D and evaluate the double integral y dA, D = {(x,y)| 0≤ x ≤ ¹,0 ≤…

A: The region D is bounded by the below curves:x=0 to x=1; y=0 to y=x3.

Q: 3. Evaluate SIS 3z dV where E is the region inside both x² + y² + z² = 1 and z = E x² + y².

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