2. Find the volume for the solid generated by taking the area enclosed by f(x)=cos(x), x=0, x = and the x-axis and revolving it around the y-axis.

Q: b- Find the volume of the solid formed by revolving the region bounded by: y=x² –1 from x =-1 to x=1…

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Q: 1) Given the region bounded by the graphs of y = x sinx ,y = 0,x = 0, and x = T, find the volume of…

A: Volume of solid =>V=∫ab2πrh.dx

Q: Set up the equation in solving volume of the solid generated when the arca bounded by z T. x = 0,…

A: This question is based on application of Integration.

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

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Q: Find the volume of the solid generated when the region enclosed between y = cos x and y = 0for 0 ≤ x…

A: The volume of the solid generated when the region enclosed between y = cos x and y = 0 for 0 ≤ x ≤…

Q: In the given equation as follows, consider the solid formed by revolving the region bounded by y =…

A: The solid is formed by revolving the region bounded by y=x , y=0 , x=1 and x=3 about x axis

Q: Q4| Find the volume generated when the area between y = cos x,y = sin x and the y - axis is rotated…

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Q: Find the volume of the solid that results when the region enclosed by y = e2", y = 0, x = 0, x = ln…

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Q: Ex/ Find the volume of solid generated by revolving the region y2 and x = y enclosed by x = 1- about…

A: You have posted multiple question. As per the instruction, we will be answering the first question.…

Q: Consider the region bounded to the right by the graph of x=sin(5y)+10y, to the left by the y-axis,…

A: Solution: The region bounded by left x=0

Q: Calculate the volume V of the solid obtained by rotating the region under y = x2 about the x-axis…

A: To find the volume V of the solid obtained by rotating under a region, use the formula, V=∫abπ(y)2dx…

Q: 3. Use the shell method to find the volume of the solid generated by revolving the shaded region…

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Q: 4. Find the volume of the solid obtained by rotating about y ax[is the re[gion between y=x^2 and…

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Q: Consider the region bounded by the graphs of y = ln x, y = 0, and x = e. c. Find the volume of the…

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Q: Find constant K, K positive, so that the volume of the solid of revolution determined by rotating…

A: we will use shell method to find volume of solid of revolution

Q: Find the volume generated by revolving the area under the curve y=e^x from x=0 to x=1 about the…

A: Volume of the solid obtained by revolving x=g(y) about x-axis is given by,                   V =…

Q: Find the volume generated by revolving the curve y = cos(2x) about the x-axis, 0 < < 4

A: Given:       y=cos(2x) , 0≤x≤π4

Q: 15. Find the volume of the solid generated by revolving y-axis, the area enclosed by the parabole y²…

A: Given y2=4ax and y=x Volume rotating about y- axis = π ∫ab x22 - x12 dy

Q: 1. Sketch the region enclosed by y = y = 0,x = 1,x = 5. Find the volume of the solid x2 obtained by…

A: Sketch the region enclosed by the given curves:

Q: 2.4. Find the volume of the solid generated by revolving the region bounded by y = 5a about the…

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Q: (b) Find the volume of the solid generated by revolving the region between the parabola, y? = x – 3…

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Q: Find the volume of the solid generated when the region en- closed between y = cos x and y = 0 for 0…

A: The volume of the solid generated by revolving the curve y=f(x) , x-axis and the vertical lines x=a…

Q: 2 - Find the volume generated by revolving the area under the curve y = e* from X= o to = ) (a)…

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Q: 5. Use the shell method to find the volume of the solid obtained by rotating the shaded region about…

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Q: 5. (6') Find the volume of the solid formed by revolving the area bounded by y = sin(x²), x E [0, T)…

A: Given - A bounded region To find - Volume of solid by revolving the region about specified line

Q: Set up the equation in solving volume of the solid generated when the area bounded by x = Vy, x = 0,…

A: Volume Of Revolution about y-axis:  STRIP METHOD:

Q: The curve y = cos x between x = 0 and x = pi/4 is rotated around the y axis, yeilding a solid, find…

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Q: 3. Find the volume generated by revolving about the x-axis in the second quadrant under the curve y…

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Q: 4. Find the volume of the solid generated by revolving the region between the y – axis and the curve…

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Q: Find the volume of the solid generated by xll – x2 = 51 revolving the curve y? between x = 0 and x =…

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Q: Set up the equation in solving volume of the solid generated when the area bounded by x = Vỹ, x = 0,…

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 2. Find the volume of the solid generated by revolving the shaded region about the given ах x+ 2y -…

A: I use cylindrical shell method for both Questions

Q: Consider the region enclosed by the curves y = x²+1 and y = 2x + 1: 5- The volume of the solid…

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Q: A solid has a base formed by y = cos(x), y = 0, x = 0, and x = , as shown below. Each cross-section…

A: To find the volume of the solid.

Q: Find the constant k>0 such that the volume of the region lying inside the sphere 2 x +y +z =a and…

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Q: Q4\ Find the volume generated when the area between y = cos x, y = sin x and the y - axis is rotated…

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Q: A solid of revolution is generated by rotating the region between the x-axis and the graphs of…

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Q: (3+In x) Find the volume of the solid when the curve y=- is rotated 360° about the x-axis between x…

A: Using disk method volume is:  V=∫ee3πy2dx     =∫ee3π3+lnx3/2x1/22dx     =π∫ee33+lnx3xdx…

Q: Find a curve such that when the portion of the curve from x = a to x = b is rotated around the…

A: Let the curve be y=fx.  The curve is rotated around X-axis from x=a to x=b.  The surface area of…

Q: Given the region bounded by the y-axis, y sin(x), and y cos(x) (up to their first point of…

A: The given region is bounded by

Q: Consider a thin rod oriented on the x- axis over the interval [0, x/2]. If the density of the rod is…

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Q: The volume of the solid generated by revolving the region bounded by the curve y = cos x, 0Sxs about…

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Q: Find the volume oF the solid OF revolution when the region below y= x+1 and between X=o aNd x= 2 is…

A: Introduction: The formula of volume of solid obtained by rotating the curve f about x-axis is given…

Q: Find the volume of the solid of revolution generated by revolving y = (e^−x) + 2around the x-axis…

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Q: 6. Find the volume of the solid obtained when the region bounded by y ==, y = 0,x = 1, and x = 2 is…

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: a) Neatly sketch (and shade in) the area bounded by 5 y = sin ¹ (F2), v y = 0, x = 0 and a = 6 b)…

A: As per the question we are given a sine curve as : y = sin(6πx/5) And we have to : Sketch the area…

Q: 1The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

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Q: 15. Find the volume of the solid obtained by rotating the region bounded by xy = 4 and y = (x – 3)…

A: Given :  xy=4  and  y=x-32. Therefore, x-32=4x⇒xx2-6x+9=4⇒x3-6x2+9x-4=0⇒x-12x-4=0Therefore, x=1 ,…

Q: 15. Find the volume by the parabole y² = of the solid generated by revolving y-axis, the area…

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