Calculate S (2x + y) dxdy, Where R is a region bounded x=y"-1,x=3,y=-1 and y=2 R.

Q: find the region bounded by x= Y-y3 ,X=1 = 1 Y=L, revolved about o X- axis

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Compute volume under the surface x+ 2y2 above the region described by 0sxs1 and 0sysx?, shown below.…

A: Given that surface is x+2y2 and region is described by 0≤x≤1 and 0≤y≤x2. It is required to find the…

Q: Evaluate y'dx+ xydy where C is the boundary of the region bounded by y = Vx.y 0, and x 9.

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Q: Calculate ff 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2 R.

A: The given integral: I=∬R4y dy dx Where I is the integral, R is the region. The region R bounded by,…

Q: Sketch the region of intearotion and evaluote. the integral. x2+y2e Vxz+ya dx dy 1n5 -n5)- y2

A: Consider the provided integral,

Q: Find the area of the region bounded by y = e* – 1,y = lnx,y = 0 and y = 2, first integrate with…

A: Step 1 :              find area bounded by  y=ex-1…

Q: Find the region bounded by the curves y = x and y = x² using a dx integral.

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Q: The region between the graphs of y=x^2  and  y=3x is rotated around the line x=3 The volume of the…

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Q: Compute volume under the surface x+ 2y2 above the region described by 0sxs1 and 0sysx², shown below.…

A: Calculate the volume: V=∫x=01∫y=0x2∫z=0x+2y2dzdydx   =∫x=01∫y=0x2x+2y2dydx   =∫x=01x3+23x23dx…

Q: Calculate the area of the region bounded by y= Vx+1 and y = x – 2x – 3. %3D

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Q: R is the region bounded by y = 4 – x2 and the x-axis and it is revolved about y = 4.

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Q: Sketch the region whose area is represented by the definite integral. dx y y y 6 1.2 1.2 1.0 1.0 0.8…

A: Here we have to find out the area graphically represented by the definite integral. ∫05x5dx

Q: Sketch the region of integration. (x, y) dx dy y y (0, 9) |(9,9) (0, 9) (9, 9) y=x y=x

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Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1?

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Q: The region R is bounded by y 4 %3D and y = x +3. -

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Q: A// Find the area of the region bounded above by (y= e), bounded below by (y x)and the boundary line…

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Q: Calculate (2x + y) dxdy, Where R is a region bounded x=y"-1,x-3, y= -1 and y= 2 R

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Q: Find area of the region bounded by x2 + y2 = 32, 6y = -7x and 15y = 4x where y > 0. Leave your…

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Q: Calculate (2x + y) dxdy, Where R is a region bounded x=y-1,x=3,y=-1 and y=2 R

A: The double integral is of the form ∫ab∫g(x)h(x)f(x,y) dxdy  or ∫cd∫g(y)h(y)f(x,y) dydx To solve the…

Q: he region bounded by x2 + y2 = 4?, 4y = -5x and 13y = 6x where y 2 0. Leave your answer correct…

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Q: Find the area of the region bounded by the graphs of the equations y = e, z = 0, z= 5, y = 0

A: To find the region bounded by the following graphs of equations,  y = ex  x = 0 x = 5 y = 0

Q: The volume of the region bounded by x² + y² + z2 =1 is

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Q: = Find area of the region bounded by x² + y² = 4², 10y = -6x and 13y 8x where y > 0. Leave your…

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Q: Find the area of the region bounded by the graphs. 1. y=x',y=Vx 2. y+x = 6, y+2x-3 = 0 3. 2y = x+…

A: Area enclosed by bounded region  y=x^2 , y=√x A=1/3 sq units

Q: R is the region bounded by x2 + y – 4 = 0 and x – y +2 = 0 and it is revolved about y = 0.

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Q: Calculate f 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2

A: Given integral is ∬R4ydydx, where R is a region bounded by the curve y=x2 and y=−3x2−2. We have to…

Q: Find area of the region bounded by x² + y² = 5², 7y = -3x and 19y = 4x where y > 0. Leave your…

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Q: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

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Q: 4. Ris the planar region whose area can be evaluated by: L,(x+ v2 – x) dx + S 2V2 – x dx. -

A: Given that, The area can be evaluated by, A=∫-21(x+2-x)dx + 2∫122-x dx We have to find the area.

Q: Integrate f(x, y, z) = x over the region in the first octant bounded above by z = 8 - 2x 2 - y2 and…

A: Given that, z=8-2x2-y2        ...(1)z=y2              ...(2)

Q: ( ) The region between the graphs of y = x2 and y = 2x is rotated around the line x = = 2. The…

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Q: Find area of the region bounded by x2 + y2 = 32, 6y = -6x and 20y = 6x where y 2 0. Leave your…

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Q: Compute volume under the surface x + 2y2 above the region described by 0<x<1 and 0 sysx2, shown…

A: See the attachment

Q: Sketch the region R whose area is given by the iterated integral. 8 (64 - y2 dx dy 60 8. 50- 6- y 4…

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Q: Find the area of the region bounded by y = 5-x2, y 2x + 2, y=-x-1, a. in terms of x b. in terms of y…

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Q: Evaluate the double integral S, x dx dy where the region R is bounded by: R 9. y = 4x – 3, y =x +, y…

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Q: Find area of the region bounded by x2 + y2 = 52, 3y = -2x and 20y = 8x where y 2 0. Leave your…

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Q: Integrate f(x, y) = x + y over the region bounded by y = 5x and y = 7x – x2. (Round your answer to…

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Q: Find the area of the region bounded by the curves x = =Dy² +2, y y = x-4 and y = 0.

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Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: Define the region bounded by y = 0, y=4Vx , y = 24 - 2x and y = X -4 using vertical and horizontal…

A: The equations of the bounding sections are: y=0y=4xy=24-2xy=x-4 The equations are plotted on a…

Q: y = 0, y = 2, y = 2 – (x + 2)´, y = 2 – x -

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Q: Sketch the region enclosed by the given curves and decide whether to integrate with respect to x or…

A: This question can be solved using application of integrals to find area under curves.

Q: Find by double integration the area of the region in xy, plane bounded by the curves y = x2 and y =…

A: Using vertical strip

Q: define the region bounded by y = 0, y = 4√x, y = 24 − 2x, and y = x − 4 using vertical and…

A: Given curves are y=0, y=4x, y=24-2x and y=x-4. We have to define the region bounded by the given…

Q: SS ez+ydydx where R is the region bounded by: r = 0, y = 0, x + y = 1. Calculate the value of

A: The given integral is ∫∫Rex-yx+ydxdy where R is the region given as x=0; y=0; x+y=1. Change the…

Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x², and bounded on the…

A: We need to calculate the intersection points of the given curves. So,…

Q: Find area of the region bounded by x2 + y2 = 6?, 5y = -7x and 2ly = %3D 11x where y > 0. Leave your…

A: The region bounded by x2+y2=62, 5y=-7x &amp; 21y=11x where y ≥0

Q: Find the area of the region enclosed by the curve y=x2-2 and by the line y BO 2. y=x²-2 y=2 Co

A: The equation of the curve is:                                            y=x2-2  The equation of the…

Q: (4-x² f (x, y, z) dy dz dx

A: Please see the below picture for detailed solution.