Consider the region in the xy-plane that is bounded by y = 3 x^2 and y=3x for x ≥ 0. Revolve this region about the y-axis Super quickly so that your eyes glaze over and it eventually looks like a solid object at one point. What would the volume of this solid be? Make sure to include every step.

Q: Find the volume of the solid generated by revolving about the line x = 3 and the region is bounded…

A: To find the volume.

Q: The region bounded by the curves y = 2x and y = x2 is revolved about the x-axis. Give an integral…

A: The general formula is                  V=     ∫abπ(f(x))2  dx-∫abπ(g(x))2  dx  where  f ( x )  is a…

Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= 1/x and x = 2. Set up the…

A: We sketch the region using a graphing calculator.  Red curve is : y=1/x Violet curve is: y=sqrt(x)…

Q: 14-X %3D (0,4) about the line y=4

A: The given equations are y=4-x, y=0,x=0 on the interval 0,4 and is rotated about the line y=4. Sketch…

Q: Find the volume of the region that results when the region bounded by the curve 4x=y^3 and the line…

A:

Q: Find the volume of the solid generated by revolving about the line y=-1 the region bounded by the…

A:

Q: The area bounded by the curve y = x,y% = 2x and y = 4 is revolved about the line x =-2 Determine the…

A:

Q: 5. Find the volume generated by revolving the region bounded by y = 9- x2 and y = 0 about the…

A: Given: The region bounded by y=9-x2 and y=0 is revolved around x axis. Let the bounded region be R.…

Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y-2= 0 is…

A: We know that if y=f(x) ,and y=g(x) are two curve intersecting at  x=a and x=b  the required volume…

Q: Consider the region bounded by the graph of y = x^2 and the line y = 4. Express the definite…

A: a)

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: nded by y=25-x2 and y = 5. Limits from -4 to 4 x axis. Use washer

A: Consider the given curve as y=25-x2 and y=5

Q: Find the volume of the solid generated by revolving the region bounded by 1 about the line x = 3…

A: Given equation y=x2-2x+2 and x=0, x=1, y=1 about the line x=3

Q: 5. Sketch the region bounded by the two curves y=10x-x* and y=x². Calculate the volume of the solid…

A:

Q: The volume obtained by rotating the region bounded by y=36-(x-3)2 and the x-axis about the line x=…

A: Given Region bounded by curve  y=36-(x-3)2, x-axis  (means y=0) about line x=10. the maximum y is…

Q: Find the volume of the solid generated when the region bounded by y = x² – x and y = x - y2 is…

A: Introduction: If the area of the ring is A=πOuter radius2-(Inner radius)2, the volume of solid…

Q: Find the volume generated if the area bounded by the curve x2 = y - 2 is revolved about the x –…

A:

Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

A:

Q: Find the volume of the solid that is bounded above by the cylinderz = x2 and below by the region…

A: Given, bounded region z=x2, y=2-x2, y=x region can be define as ∫∫x2dxdy now region is y=2-x2, y=x…

Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: Find the volume generated if the area bounded by the curve y=x^2 and the line y=2x+3 is revolved…

A:

Q: Find the volume of the solid generated from revovling the area of the region bounded by the curve y…

A:

Q: Find the volume of the area bounded by the line y = 3x + 4 and the curve y = x² if it is revolved…

A:

Q: Set up an intergral for the volume of the solid obtained by rotating the region bounded by the given…

A: Use the method of cylindrical shells. The graph of the bounded region is given below.

Q: ut the line x = 3.

A: The parabola equation is given , x2 = 4y. The equation of line is given , x = 4 - 2y. The volume…

Q: Set up the integral that represent the volume of the solid obtained by rotating the region bounded…

A:

Q: Find the volume of the solid form by the region bounded by the lines y = 16 – x, y = 3x + 12, and x…

A:

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: Volume integral problem.....

Q: Find the volume (in cubic units) of the region bounded by the curves y= Sin x ,and y= cos x and the…

A: The solution are next step

Q: The region bounded by the parabola y = x and the line y = 2x is revolved about the line y = -1. Find…

A:

Q: The region bounded by the curve y = x and the line y = 3x, is revolved about the line x=-3. Find its…

A: Given functions are                                                         y=x2y=3xx=-3 points of…

Q: Determine the volume of the solid (NX6. 2) obtained by revolving the region bounded by x + 2y² + 3 =…

A:

Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

A:

Q: What is the volume generated when the area bounded by y=2x2+1; x=1; x=2 is revolved about the line…

A:

Q: Find the volume of the solid generated by revolving about the line x = -4 the region bounded by the…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graph 1 4x -x4, the y-…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: When we calculate the volume of solid obtained by rotating the region bounded by the curves y = 2x²…

A: Given:       Curves y=2x2                   y=2x and line y=2 Volume of solid V=π∫abfx2-gx2dx

Q: Find the volume OF the solid Formed by revolving the region bounded by the graphr of x- -y't 4y, and…

A:

Q: Find the volume generated by the region bounded by the curve 4x = y² and the line x - 4 = 0, rotated…

A:

Q: find the volume of solid generated when the regions enclosed between the curves y=x^2 and x=y^2 is…

A: Given curves, y=x2andx=y2 To find the volume of solid generated by these curves about x - axis.

Q: Find the volume (in cubic units) of the region bounded by the curves y' = 4x and the line X = y when…

A:

Q: Determine the volume of the solid generated when the region bounded by the curve y²=x³ and the…

A: It is given that curves are y2=x3 and y=0 (i.e. x-axis) If these curves are drawn on a graph, they…

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: Find the volume of the solid obtained when the region enclosed by the curve x=2-y² and find the x=y…

A: Draw the sketch of the given curve and lines.

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

A:

Q: Sketch and set up the integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13,…

A: Given are the curves  y=x2+x-2 and y=3x+13 We need to set up the integral for the volume of the…

Q: Find the volume of solid formed when the region bounded by y = x² and y = Vx are revolved about…

A: To find the volume of solid formed when the region bounded by y=x2 and are revolved about x-axis…

Q: Find the exact volume generated by revolving the region bounded by f(x) = 2x^2 + 10 and g(x) = 4x +…

A: The volume generated by revolving the region by line y= 10 The given functions are fx=2x2+10 and…

Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

A: