a) Find the area between y = 3x2 – 4 and y = 6x + 5. - b) Find the volume of the solid whose base is the triangle enclosed by y-axis, y = 3, and y = x, and the cross sections perpendicular to the x-axis are semi-discs above xy-plane.

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

A: If  you like the solution then please give it a thumbs up.. The Answer is:     Volume = 4π3

Q: Find the volume of the solid of revolution formed by rotating the region bounded by the parabola…

A:

Q: Find the volume of the solid obtained by rotating the triangle with the vertices A(0,0), B(4,4) and…

A: Solution

Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Given

Q: 3. Use cylindrical shells to find the volume of the solid eenerated when the shaded region is…

A:

Q: Determine the volume of the solid of revolution which is formed when the area bounded by x = 0, y =…

A: Given curves are: fx=y=arctanx ; x=0 & y=1 From the dentition of the inverse function, we can…

Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Use the Theorem of Pappus to find the volume of the solid of revolution The torus formed by…

A:

Q: Find the volume of the solid of revolution bounded by y = 1/(x+1), x = 0, x = 2, and the x-axis, and…

A:

Q: The volume of the solid generated by revolving the region bounded by y = 2x - x² and (5a+1)π y = 0…

A: Volume

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: 4. Determine the volume of the solid obtained by rotating the portion of the region bounded by y =…

A:

Q: Find the volume of solids figure generated by rotating the area between y = 4x - 1 and thex- axis…

A: Given- The figure generated by rotating the area between y=4x-1, x-axis and the lines x=1 and x=3…

Q: 1- Find the volume of the solid generated be revolving the shaded region about the given axis. About…

A: The volume of the solid generated when the first given region is revolved around the y-axis is to be…

Q: Determine the volume of the solid obtained by rotating the portion of the region bounded by…

A: First we have to plot the given region.

Q: b) Determine the volume of the solid generated by rotating the region bounded by y = V2x and y =…

A: We have given the curves

Q: B. Find the volume of the solid generated when the plane region bounded by 4. y =, x = 1, x = 4, and…

A:

Q: 4- Find the volume of the solid generated by revolving the region about y-axis,the region in the…

A: Draw the graphs of y=x2, x=2 and identify the region bounded by the curves. The required region is…

Q: Exercise 5: Find the volume of the surface of revolution generated by revolving the region bounded…

A:

Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

Q: Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed…

A: y = 8−x² given y = x²     given This means that 8- x² = x² 2x2=8 x=-2,+2 Then, y=4,4

Q: The volume of the solid obtained by rotating the region enclosed by y=x3, y=16x, x≥0   about the…

A: to calculate the required volume of revolution

Q: Determine the volume of the solid of revolution which is formed when the area bounded by x = -4.5, x…

A:

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 4), and (2, 0).…

A: Given vertices of the triangular base is 0,0, 0,4 and 2,0. We know the equation of the line passing…

Q: Use the disk method to find the volume of the solid of revolution bounded by the graphs of f(x) =…

A:

Q: Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by…

A: We have to use theorem of pappus to find the volume of solid of revolution The torus formed by…

Q: The volume of the solid bounded below by the xy-plane, on the sides by p-33, and above by

A:

Q: Find the volume of the solid enclosed by y = x² + 1, y = 9 – x² and rotated about the y-axis.

A: Suppose a region is enclosed by two curves y=fx and y=gx. To calculate the volume of the region…

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

A:

Q: Use the Theorem of Pappus to find the volume of the solid of revolution The solid formed by…

A: Theorem of Pappus: The volume of solid of revolution generated by revolving a lamina about an axis…

Q: Find the volume of the solid whose base is the triangle enclosed by y-axis, y = 3, and y above…

A: First draw the base of the solid and find the cross section area then integrate.

Q: The region bounded by f(x) = - 3x? + 15x + 42, x = 0, and y O is rotated about the y-axis. Find the…

A:

Q: find the volume,The region bounded in back by the plane x = 0, on the front and sides by the…

A: Given

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: Determine the volume of the solid of revolution which is formed when the area bounded by x = 0, y =…

A:

Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

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: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: Given: The equation of the curve is The region is rotated about x-axis. The volume of solid…

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 7+x…

A:

Q: (b) Use Disc method to find the volume of the solid formed by revolving the region bounded by f(x) =…

A: Integrals and derivatives are considered as inverses of each other. For example if we have a…

Q: (c) Find the volume of the solid generated by revolving the region enclosed by the triangle with…

A:

Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=1, and the cross…

A:

Q: 2. Find the volume of the solid generated by revolving the plane region bounded by .2 x2 + 16 1 %3D…

A: Answer

Q: Find the volumes of the solids generated by revolving the region between y= 3/x and y= about a) the…

A: Given the solid generated by revolving the region between y=3x and y=x24

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: (b) The volume generated by i. rotating the area enclosed between y = 1- 2² and y = 0 by the y axis.

A: Given that the area is between curves y=1-x2 and y=0. Rotated about y-axis.

Q: A cone of height H with a base of radius r is cut by a plane parallel to and h units above the base,…

A:

Q: Find the volumes of the solids generated by revolving the region between y = 2/x and y = about a)…

A:

Q: Find the volume of the solid whose base is the semicircle y = v9 – x2 where -3 < x < 3, and the…

A: