4 The area of the surface S = {(x, Y, z) E R³ : z = 5 – x² – y², z > 3} equals (A) 4ñ 9. (B) 5* 13 (C) 3 8 (D) 3

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: 1. The solid in the first octant bounded by the coordinate planes and the surface z = 1- y – x2.

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Q: w= Pcxiy,Z) = In (x+y+2) ,x= cost, and z = 4VE %3D 2X = y= Sint >use ch ain rule to Rind du in terms…

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Q: raluate the double integral R 3ædA where Ris the triangle with vertices (-1,0), (0,1) and (1,0).

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Q: AIS. 4. Compute the area of the surface formed when f(r) = 2 + cosh(r) between 0 and i is rotated…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: 1. Find the area of the surface z = k + xy inside the cylinder x² + y² = R² for constant R. k > 0 is…

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Q: Find the potential u(x, y) for u +u =0 in the rectangle 0<x< 2 and 0 < y s 2, if the upper side is…

A: The given problem is to solve the potential u(x,y) Laplace partial differential equation, we have to…

Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: 8. (x – y) dV, where E is enclosed by the surfaces z = x² – 1, z = 1 – x² , y = 0, and y = 2 E

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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: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

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Q: 2 3 3 Find the area of the surface z = = X2 + y2 3 where 0 < x 1, 0 < y < 1

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Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

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: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: 8. Evaluate the line integral x dx + xedy where C is the closed path along the triangle in the…

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Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

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Q: 2 (2y-y² 15. Evaluate the integral / x² + y²dzdydx by using cylindirical coordinates.

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Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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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: V = 200 /R volts in free space in the region bounded by 2mm <R <3mm, 0 <8 <n / 2 and 0 <o <n / 2…

A: Given 2 mm&lt;R&lt;3 mm, 0&lt;θ&lt;π2 and 0&lt;ϕ&lt;π2 Now, 2×10−3 m&lt;R&lt;3×10−3 m And under…

Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

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Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

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Q: No. Date Evaluate fff dv G x² + y² where G is a solid that lies inside cylinder *+(4-2)² =4 obove…

A: we will use cylindrical co ordinate system to solve the given integral

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: || | /3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8. %3D

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Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

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Q: 1 Find the centroid of the area bounded by x2- 4y + 8 = 0, the lines x = 0 and x = 4, and the…

A: Formulas are written within the solution.

Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

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Q: E is the region behind the surface y = 4 – x² that is in front of the region in the xy-plane bounded…

A: Given integral: ∫∬E18x dV Given that E is the region behind the surface y=4-x2 that is in front of…

Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: 8K Use Green theorem to eva luate the . line integral : 3. 3 where c is ニ thecircle

A: Given the line integral

Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

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Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

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Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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Q: 24) The area of R3 using horizontal strip is y = x² A. rdx А. R2 B. (x-x kcx D. [ 5-1kv 25) If R2 is…

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Q: 12. Find the outward flux of F = x*yi-cyj+zk across the boundary of the region which is bounded…

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Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

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Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

A: