Evaluate the double integral Sre+2vdA, where R is the triangle with verices (0,0), (2,0) and (2, 2). Sketch the region. 2. y 20T V

Q: Evaluate the triple integral R. where R is the region enclosed by the sphere r2 + y² + 2? = 9.

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Find the integral ſf x²ydxdy, where the region Ris the segment of a circle. The boundaries of the…

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Q: Evaluate the integral (x² + y² + z² )0.5 dV where D is the region within the cone z = x² + y² and…

A: Consider the provided question,

Q: The double integral 2xycosydA over the rectangular region R= {(x,y) E R2, 0<x<1 and 0 sysn} is equal…

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Q: Let B be the region in the first octant inside both x? + y + z? = 1 and x² + y² . a) Find the triple…

A: Let's find given all triple integrals.

Q: Find the centroid of the region bounded by y? = 28x and y? = 56(x – 14). NOTE: Enter the exact…

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Q: Evaluate dA where R is the region given by 0sxs 1, 0s y s 1.

A: The question is taken from the calculus in which we have to find the double integral value  so We…

Q: Evaluate the surface integral. xz ds S is the boundary of the region enclosed by the cylinder y? +…

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Q: Consider a region R, which lies above the x-axis and between the circles x² + y? = and x? + y? = n²…

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Q: Evaluate the double integral ∫R∫ f(r, θ) dA and sketch the region R.

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Q: Find the centroid of the region bounded by y? = 14x and y² = 28(x – 7). | NOTE: Enter the exact…

A: The centroid coordinates are given by x¯=1A∫Ax dA and y¯=1A∫Ay dA.

Q: Find the volume of the region bounded above by the paraboloid z=x? + 3y2 and below by the square R:…

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Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: 1. Find the area in the first quadrant, cut from the cylindrical surface x2 + y2 = a2 the plane z =…

A: Consider the given information: The surface is given by, x2+y2=a2 and the plane z=x.

Q: Q: Sketch and find the area between y = x² and y = Vx, %3D using double integral. ( find S dxdy , SS…

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Q: Evaluate the double integral. I| 4y² dA, D is the triangular region with vertices (0, 1), (1, 2),…

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Q: Consider the double integral (æ+1)² + (y – 1)² = 2 R R Where R is the region of Xy given Find the…

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Q: answering this question. Please you specify each step and for ble. ank You. me of the region between…

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Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, –2, 0),…

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Q: Evaluate the double integral. / 7(16 + y²) ¯ dA; R. R is the region in the first quadrant enclosed…

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Q: A solid is formed by rotating the area bounded by z+y 6 and y r about the line y=-3. Using washer…

A: A solid is formed by rotating the region bounded by x2+y=6 and the line y=x about the line y=-3. The…

Q: Find the centroid of the region bounded by y? = 22x and y? = 44(x - 11). NOTE: Emter the exact…

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Q: If R is the region enclosed by x-axis, y = -3x and x = -2, then evaluate the following double…

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Q: Find the double integral ∬R(x+y)dxdy, where the region R is a parallelogram with the sides y=x,…

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Q: Evaluate, . (y+2x)dV where E is bounded by the parabolic cylinder y = x and the planes y = x - 2, z…

A: Given: E is bounded by the parabolic cylinder y2=x and the planes y=x-2,z=y and z=0 Then we have to…

Q: Evaluate the double integral +ydA, where R is the rectangular region defined by R-((x.y)-1sxS0.0…

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Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, -2, 0),…

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Q: Find the centroid of the region bounded by y? = 32x and y? = 64(x – 16). NOTE: Enter the exact…

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Q: (c) By using double integrals, find the surface area of plane 2x + 5y + z = 10 that lies inside the…

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Q: Evaluate J xy dA¸ where Ris the region in y =x? 2 A 13/7 16/3 18 D) 20 B.

A: To find : ∬xydA where  R is the region of y=x2 and y=0

Q: Find the centroid of the region bounded by y? = 28x and y? = 56(x – 14). NOTE: Enter the exact…

A: In order to calculate the centroid of a region it is needed to find the area of the region bounded…

Q: Find the volume inside the sphere (r = a) that lies between the cones ($ = n/3) and ($ = 2n/3) %3D…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: ate the surface inte S, where S is the (x³/2 < x <1 and 0 < ce z = 3 се z (x3/2 + y

A: We have to choose the correct answer from the given options according to the given condition

Q: Find the volume of the region bounded above by the paraboloid z = x? + 4y? and below by the square…

A: We have to find the volume of the solid bounded above by the paraboloid z=x2+4y2 and below by the…

Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x² + y? =…

A: Given Surface area (S) is Region is In polar coordinates

Q: Q4. Let R be the annular region lying between the two circles x² + y² = = 1 and x² + y² = 16.…

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Q: Let B be the region in the first octant inside both x? + y + z? = 1 and z = Vx2 + y² . a) Find the…

A: Given,x2 + y2+z2 = 1          __________(I)and z = x2+y2        ____________(II)Putting (II) in…

Q: Use a triple integral to find the volume of the solid enclosed between the elliptic cylinder a² +…

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Q: R= {(x.y) x+y²>1, DEx<1, Osysd} draw the region and calculate the integral on that region dA

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Q: Evaluate /VT² + y² dV_where E is the region that lies inside the cylinder E x² + y? = 4 and between…

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Q: 9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle R =…

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Q: Q: Sketch and find the area between y = x2 and y = Vx, %3D using double integral. ( find ſſ dxdy ,…

A: We need to sketch the region between the given  curve and also have to calculate the area using…

Q: raluate the surface integral. xz ds S is the boundary of the region enclosed by the cylinder y2 + z2…

A: S is the boundary of the region enclosed by the cylinder y^2+z^2=9 and the planes x=0 and x+y=8 S1:…

Q: Evaluate the surface integral. x ds, S is the triangular region with vertices (1, 0, 0), (0, -2, 0),…

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Q: Consider the double integral S SR x²y dA, where R is the semicircular region given by {(x, y) [x? +…

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Q: Find the centroid of the region bounded by y? = 22x and y² = 44(x – 11). NOTE: Enter the exact…

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Q: Consider the region R shown in the following figure, which involves the curves of equations 72 x2 +…

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Q: Evaluate, |.(y+2x)dV where E is bounded by the parabolic cylinder y = x and the planes y = x- 2, z =…

A: we have to draw the graph of the curves y2=x, y=x-2, z=y and z=0  we have to evaluate the…

Q: 4. Find the volume of the region E = { (x, y, z) ; x2 + y? + 22 Va2 + y?} Hint: The surface x2 + y?…

A: Volume of the given solid which bounded by the two given curve: