Consider the region enclosed by y=x2 , the y-axis, and y=1. Set up the integral of the volume of the region of space when rotated along the x-axis and y-axis.

Q: Find the volume of the solid that results when the region bounded by x = y and x = y + 12 is…

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Q: Find the volume of the region bounded by y = 1 − x 2, z = 1,y = 0, and z + y = 2.

A: We know that volume V of a region W is, V=∫∫∫Wdxdydz

Q: Find the volume obtained by rotating the bounded region defined by y = Vx y = 0 , and x = 4 around…

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Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = Va, x…

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Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = Vx, x…

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Q: Find the volume of the solid whose base is the region enclosed by y = x² and y 3, and the cross…

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Q: . Find the volume of the solid obtained by rotating the region bounded by  y = √x    x = 0, and x =…

A: Given curve y=x, x=0 and x=4. The volume is generated by curve rotating about x-axis.

Q: Let R be the region bounded by the graphs of y= Vx, x= 9 and the x – axis, then the volume of the…

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Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = 3T, x…

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Q: Find the volume of the solid generated when the region enclosed by y = \2x + 8, y = x, x = 0 is…

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

Q: Find the area of the region bounded by the given curves and find the volume of the solid formed when…

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Q: Find the volume generated by rotating the region between the graphs of x = sqrt (y) , x = 0, and y =…

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Q: p3y 8–x²-y² dzdxdy 0.

A: We solve triple integration using ordinary method

Q: Find the volume of the solid generated when the region enclosed by y = Vx + 1, y = V5x, and y 0 is…

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Q: What is the volume of the solid R bounded by the x- axis, x = 1, and y = sqrt(x) when R is revolved…

A: We have,  Volume solid region  V = π∫ab(R2 - r2) dx Where, R = Outer radius is the distance from the…

Q: ) Find the volume formed by rotating the region enclosed by: x = 3y and y = x with y > 0 about the…

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Q: Find the volume V of the solid S that results when the region bounded by y = x2, y = x, x = 0 and y…

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Q: For the area bounded by y2=4x and y=x, find the volume generated if it is revolved about the line…

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Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^2, y=1,…

A: We will integrate cross sectional area of any x to get the volume of solid.

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by…

A: We have to find the volume of the solid obtained by rotating the region bounded by y=2sqrt(x) ,x=0…

Q: Find the volume of the solid generated when the region enclosed by y=x^3, x=1, and y=0 is revolved…

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Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y = x°, y =…

A: We have to determine volumes of solid

Q: Find 2xdA over the region R R = {(x, y) | 0 < æ < 4,0 < y < 2F by indentifying it as the volume of a…

A: Consider the given integral as ∫∫R2xdA

Q: Find the volume of the region bounded above by the paraboloid z = x2 + y2 and below by the square R:…

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Q: Find the volume obtained by rotating f(x) = x(1 – x) around the x-axis.

A: Given             f(x)=x(1-x) and y=0

Q: Find the volume of the solid obtained by rotating the area in the first quadrant bounded by y = x^2,…

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Q: Consider the region bounded by y = x and y = Vx, shown below. Find the volume of the solid obtained…

A: This question is related to definite integration, we will solve it using given information.

Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=4, and the cross…

A: Given: Region enclosed by y=x^2 and y=4. And the cross sections perpendicular to the y-axis are…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x² , 0, and a = 4, about…

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Q: Consider the region bounded by y = x², y = 2x Write, but do not evaluate, an integral to find the…

A: To write an integral to find the volume of the solid whose base is in the below-bounded region and…

Q: Find the volume formed by rotating the region enclosed by: 5y and y = x with y > 0 about the y-axis…

A: Given Data The first equation is x=5y. The second equation is y3=x.   Equate the given both…

Q: Find the volume of the region enclosed by z = 1 – y and z = y² – 1 for 0 < x < 42. - V =

A: To find the volume of the region enclosed by z=1-y2 and z=y2-1 for 0≤x≤42

Q: Find the volume of the region bounded by y=x^3 and y=x rotated about the x-axis.

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Q: find the volume generated by rotating the region bounded by the curves x = Vỹ, x = 0, and y = 8…

A: given curves are x=y, x=0 and y=8 find the volume

Q: What is the volume of the solid R bounded by the x- axis, x = 2, and y = x2 when R is revolved…

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Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^5, y=x,…

A: The solid base is in the first quadrant which is bounded by the curves y=x5, y=x, y=1 and y-axis.…

Q: Find the volume of the solid whose base is the region bounded between the curves y = x and y = x²,…

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

A: The graph is where red curve represents y=x and blue line represents y=x.

Q: Find the volume of the solid obtained by rotating the region bounded by y=x^4 and y=1 with 0 being…

A: We have given

Q: Sketch the region bounded by the graphs of the equations y=Vx; and y=: and find volume of the solid…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5,…

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Q: Find the volume of the solid generated by rotating the area bounded by the y=sqrt(x-1) and y=(x-1)^2…

A: Given:y=(x-1)    and    y=(x-1)2 To find out: The volume generated by rotating the area bounded by…

Q: Find the volume of the solid obtained by rotating the region enclosed by the curves…

A: Given problem:- Find the volume of the solid obtained by rotating the region enclosed by the curves…

Q: Find the exact volume of the solid whose region is bounded by y = 2 a + 2, y = 0, x = 3 and x =…

A: Given data : y=2x+2 , y=0x=3 , x=4

Q: Find the volume of the solid obtained by rotating the region bounded by y = 6x?, x = 1, and y = 0,…

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Q: Use the disk/washer method to find the volume of the solid generated when the region bounded by y =…

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Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x+1), y = sqrt(5x), and…

A: The volume of the region bounded by the curves y1(x) and y2(x) is given by the formula…

Q: the

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Q: Find the volume of the solid formed f(x) Vx, y = 0, X = %3D about the x-axis.

A: Here we have to find the Volume of the solid formed by revolving  the region bounded by,  f(x)=√(x),…

Q: use the washers method to find the volume (in units3) when the region bounded by curves y=x+2,…

A: In this question we will use basic of calculus i.e volume bounded by curves rotating about x axis.…