2.) a) Sketch the region enclosed by the given curves. x = 1 – y; x =y – 1 b) Decide whether to integrate with respect to x or y. Explain your reasoning. c) Draw a typical approximating rectangle and label its height and width. d) Then find the area of the region.

Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 VI – 49x2 NOTE: Enter the exact…

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Q: Find the volume of the region U defined by the inequalities 0≤z≤2,0≤y+z≤5,0≤x+y+z≤10.

A: Obviously, this region is a parallelopiped. It’s convenient to change variables in such a way to…

Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

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Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

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A: x^2+y^2+z^2 <=64, y>=0

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A: Given, r=3θ,  0≤θ≤5.4

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A: Given that T is the first-octant solid region bounded by the below equations: y=5x2+z2y=5y=45z=0x=0…

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A: We have to find centroid of given bounded region.

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Q: Sketch the region enclosed by the given curves andfind its area.   y  = 1/x,  y =x ,    y =1/4x  ,…

A: y  = 1/x y =x     y =1/4x and x&gt;0 Formula: Area enclosed between the curves y=f(x) and y=g(x) on…

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x), y = 0, and x = 49 is…

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Q: Sketch the region enclosed by the given curves. y = 3/x, y = 12x, 1. y = -X, 3 x >0 y y 8- 6. 6. 4 4…

A: Given curves: y=3x, y=12x, y=x3 Andx&gt;0

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A: Sketch the base of the solid as follows.

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A: The volume of a solid formed by revolving the region bounded by the curve y=f(x) and the x axis is…

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A: This problem belong to circle and line section from geometry and we solve this using the second…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: Use the Theorem of Pappus and the fact that the volume ofa sphere of radius r  is 4/3πr3  to find…

A: We have, The volume of a sphere is V=43πr3                               ⋯⋯1. The semi-circular…

Q: Find the volume of the solid that results when the region enclosed by x = y² and x y is revolved…

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

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

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Q: 2. Find the volume of the solid that results when the shaded region is revolved around the Y - AXIS.…

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Q: integrate ƒ over the given region.Quadrilateral ƒ(x, y) = x&gt;y over the region in the first…

A: Given,

Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

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Q: 1. SSR ry? dA, where R is the region in quadrants 1 and 2 bounded by the semicircle of radius 2…

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Q: Sketch the region enclosed by the curves and find its area. 2 x = 0, y = 1, y = e? X = -

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A: To find the volume of the solid whose base is bounded by the given circle and whose cross-sections…

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Q: Show that the rectangular box (including the top and bottom) withfixed volume V = 27 m3 and smallest…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Sketch the region enclosed by the given curves. y = 4/x, у %3D 16х, y = -х, 16 y y 10- 10- 8 8 6. 6.…

A: Given:

Q: 1. Use the cylindrical shells to find the volume of the solids generated when the shaded area is…

A: The volume of solid of revolution can be calculated using the cylindrical elements. The formula for…

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Q: 8. Find the volume of the solid that results when the area of the region enclosed by y = 2x2, x = 2,…

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Q: Let M be the region in the first quadrant bounded by the graphs of y=arctanx and y=(πx)/4. What is…

A: Given, y=tan-1xy=πx4 Revolving around x=2   To find: The volume of rotation of the bounded region.…

Q: Find the volume.

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Q: 23. y = 2x, y =}r

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Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

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Q: Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y =x, x>0 16 y y 10| 10- 8 6. 2 4…

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Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

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Q: (b) Determine the volume of the solid that results when the region enclosed [2] by the curves y = x²…

A: Solution:Given   y=x2+2   and y=4-x2and th line y=3To determine the volume of the…

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A: Consider the graph:

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