49. Consider the region R bounded by the graphs of y = f(x) > 0, x = a > 0, and x = b> a. If the volume of the solid formed by revolving R about the y-axis is 27, and the volume formed by revolving R about the line x = -2 is 10m, find the area of R. y= fx) R

Q: 26 Find the area of the region bounded by, c. The curve y= In x, the lines x 4 and the x-axis. d.…

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Q: 2. Find the volume of the region bounded by y = vx and y 4x rotated about the x-axis.

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Q: 4 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

A: See below attachment.

Q: 1. Sketch and find the area of the region bounded by y = In x, y =1- x and y = 2.

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Q: 2. Find the volume of the solid generated when the region bounded by y = x? - x and y = x – x² is…

A: For calculating the volume of the solid revolution about particular axis, we will find the original…

Q: What is the volume of the solid whose 1 30 cross-sections are squares perpendicular to the x-axis…

A: Given: The region bounded by the curves are: y=x and y=x The cross-sections are squares…

Q: 7. Find the radius of gyration of a plate covering the region bounded by y3,x 2, and the x-axis with…

A: Formula used:Radius of gyration, moment of inertia and area under curve with reference to y axis is…

Q: 22 Find the Volume of the Solid of revolution bound al by the circuit x*+y=16, aud the lineSX=0 and…

A: Equation of the circle is given as x2 +y2 = 16 x2 +y2 = 42 Where radius of the circle r is 4 unit…

Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

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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: 1- Find the area of the region enclosed by the line y=4x and the curve y=x'+ 3x'.

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: || 2. Find the area of the region enclosed by the curves x = 2y² – y + 1 and x y² + y + 4.

A: The area between two curves is given by: Where a and b are intersection points of the curves f and…

Q: 10. Find, among all right circular cylinders of fixed volume V, the one with smallest surface area…

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Q: 1. Find the area of region bounded by the curves y = x² and line y=x. %3D

A: We have to determine area of region

Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

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Q: 1) Compute the volume of the solid obtained by revolving around the r-axis by 27 (ie. a full…

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

Q: 1. Find the area of the region enclosed by the line x = 2y and the curve x = y - y?

A: We will find out the required area.

Q: Find the volume (in cubic units) of the region bounded by the curves (y – 1)° = x – 1 ,and the lines…

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Q: Let O denote the region in a circle centered at the origin of radius 1 that is bounded from above by…

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Q: .2 What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis…

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Q: 3 Find the area Of the indicated region. between y=X and y= x2For x 'in

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Q: A region is bounded between x = 0, y = 1, x = 1, and y = (x-1)^2+1. What is the volume generated if…

A: *to find:- generated volume about x-axis.

Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 17) Find the total areas of the regions bounded 17.1) y = e", y = e(2 – x), y axis |

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Q: 14. Find the volume tended by the graph of f(x, y) = 1+2x + 3y, the rectangle [1, 2] x [0, 1], and…

A: Given function is: fx,y=1+2x+3y and the coordinate of the rectangle is: 1,2×0,1

Q: 4. Set up a (sum of) definite integral(s) that is equal to the volume of the solid whose base is R…

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Q: 2. Find the volume of the region bounded by y = x3 and y = x rotated about %3D the x-axis.

A: In this problem we can use washer method to find the volume of the solid of revolution. Washer…

Q: 2) Find the volume generated by the area bounded by y = x², y = 4x, revolved about x-axis.

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Q: 1. Find the area bounded by y= (11 - x)1/2, the lines 3x = 2 and x = 10, and the X-axis. 2. Find…

A: The given problem is to find the area between given curves and also find the volume of solid…

Q: 9. Consider the region bounded by the curves y = e", y = e¬¤ and y = 2. %3D

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Q: Find the volume of the solid obtained if the region bounded by the graphs of y = \x , y =0, and x=9…

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

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Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

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Q: Sketch the region enclosed by the curves x − 5 = 4y and x − 21 = (y – 4)², and compute its area. A

A: The given curves are; x-5=4y and x-21=y-42 Now find the point of intersection between the given…

Q: 4. Compute for the volume of the solid formed by rotating the shaded area about the x- axis. * 30-…

A: Given: f(x)=25-x2

Q: 8 Determine the area of the region bounded by the curves y = =, y = 2x and x = 4

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Q: 9) Find the volume of the region bounded by y = x + 1 x +1' Y = 0, x = 0, and у %3D0, х%3D x = 4…

A: The formula for the washer method around the x-axis is V=π∫abf(x)2-g(x)2dx where f(x) is the top…

Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Given that, The curves are y=x2+5 and y=-x2, the line x=3, and the y-axis. Find the area bounded by…

Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and ,x=-2 and x=-5?…

A: Area under curve

Q: Consider the region in the xy-plane that is bounded by y = 3 x^2 and y=3x for x ≥ 0. Revolve this…

A: Let the region in the xy-plane that is bounded by y=3x2 and y=3x for x ≥ 0.  We have to revolved…

Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

Q: 2. Find the volume OF solid obtained by revoluing region bounded the about x- axis x2 and the the by…

A: Given that, the curve is y=x2 and the lines are x=0 and x=2. Note that, the formula for the volume…

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y-y3, x…

A: Consider the graph:

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x² +1, y =…

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Q: y=√x, x = 4, and the x-axis.

A: Consider the given function y=xand the x-axis

Q: 5. Determine the area of the region bounded by y = 2x2 + 10 and y = 4x + 16. 28 24 y= 4x+16 20 16 y=…

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