2) compute the volume to : A) z = x² ,z = 1,y = 0 and y = 2 B) z = y? , z =1,2x +z = 4,x = 0

Q: Find the volume of tetrahedron with vertices (0,0,0),(1,0,0),(0,1,0)and (0,0,2) by triple integral?…

A: We have to find the volume of the tetrahedrane with vertices 0,0,0, 1,0,0, 0,1,0 and 0,0,2 by triple…

Q: 5. Find the volume of the solid enclosed by z = 4, y = 0, y = 25 – x2, and z + y = 29.

A:

Q: Find the volume of the intersection of the unit ball {(x, y, z) : x² + y² + z2 < 1} and the cylinder…

A:

Q: A/ Find the volume generated by revolving the area bounded by x = y-1 and y =5 around the x-axis?

A: We will find out the volume of solid of revolution by shell method.

Q: Find the volume generated by rotating the given region about the specified line. R, about AB

A: On revolving the region R1 around the line Ab, the resulting solid obtained will be a cone.   This…

Q: The volume of the solid under the plane 4 x+ 5 y - z=0 and above the region enclosed 27 by y= 3 x…

A:

Q: FIND THE VOLUME GENERATED BY REVOLVING THE AREA BOUNDED BY THE GIVEN CURVES AND LINES

A: Given curves equation is x2-y2=9 ⇒ x2=y2+9 ⇒ x=y2+9   ⇒ fy=y2+9  and line equation is  y=2x-6    ⇒…

Q: use shell methed to the volume by rotating the region under y=x 0ver [1,4] about X= -3.

A:

Q: 2- Use the shell method to find the volume of the solids generated by revolving the shaded region…

A:

Q: Find the volume of the solid bounded by: æy = 2, y = 0, æ = 2, and a = 4 a. about x = 1

A:

Q: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

A: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

Q: Find the volume generated by revolving the area 1 bounded by y 3, x = 4, and y = 0 about the y-axis…

A: Solution

Q: Prove that the volume of a segment of height h of a sphere of radius r is V = }nh°(3r – h)

A:

Q: Find the volume generated by revolving the area bounded by x +y=2, x - y = 4, and y +3 = 0 about x =…

A: Given Area bonded by x+y=2, x-y=4 and y+3=0 about x=y So figure is Since all the rectangular…

Q: Derive the general formula for volume of x = x3 , x-axis, x = 8 by circular disk method

A: Given: The region bounded by the curves are x3, x-axis, x=8 we have to find the the volume by…

Q: The volume of the solid under the plane 3 x+ 3 y -z=0 and above the region enclosed 23 by y=2 x and…

A:

Q: If the path defined by z(x) from points C to W were rotated about the x-axis, what would be the…

A: Given zx=-0.00001x6+0.00026x-0.00313x4+0.01704x3-0.01298x2-0.30265x+3.56157 To find the volume of…

Q: Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal…

A: • To solve this problem, we have to express the total surface area of the cylindrical can in a…

Q: What is the volume in the first octant bounded by x² + y – 4 = 0 and z = x. Use a triangular…

A:

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y? = 4x, about the…

A: Given curves are y=x, x=1   and  y2=4x We have to calculate the volume generated by these curves…

Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

A:

Q: Find the volume generated by rotating the area bounded by y = ,* = 2, x = 7, and y = 0 about the y…

A: The solid obtained by rotating the region between the grah of fx and the x-axis from x=a to x=b…

Q: Use the theorem of Pappus a = 2 is positioned with the Volume = %3D Write as an exact expressi

A: .assume that a disk of radius a=2 is positioned within the left hand of the circle  at x=b=9 and is…

Q: Find the Volume enclosed by N = x2+y² and

A:

Q: In order to find the volume obtained by revolving the region enclosed by y = Vxe-* and y =…

A:

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A: I am attaching image so that you understand each and every step.

Q: Evaluate the volume of the following solid. ZA 1 z = 1- x? 1 y = 1– x 1

A:

Q: What is the volume in the first octant bounded by x2 = 16 – y and z + y = 16.

A: Given curves are

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: Find the volume of the region E 3 = {(x, y, z) : æ² + y? – 3 < z < v 9 – x² – y² } - - -

A:

Q: What is the volume in the first octant bounded by x2 + y − 4 = 0 and z = x. Use a triangular…

A:

Q: Find the volume generated by rotating the area bounded by each set of equations around the x-axis.…

A: The volume for solid of revolution for a curve is the volume of object determined by a curve fx…

Q: Determine the volume of a four dimensional unit sphere: x, =r sin 8, sin 8, cos p, x, =r sin 0, sin…

A: The given problem is to find the volume of four dimensional unit sphere, we have to set up an…

Q: Find the volume V which lies inside the sphere x^2+y^2+(z−4)^2=16 and outside the sphere…

A:

Q: Calculate the volume of a bounded solid. 3) a? + 3? + 2? = 4 ,a² + y? = 2? Draw the region over…

A:

Q: Determine the volume generated about y = 4, the area bounded by x + y = x? %3D and x? + y = 3.

A: To find the find the volume about y =4 Given x + y = x^2 , x^2 +y = 3

Q: use a theorem of Pappus to find the volume generated by revolving about the line x = 5 the…

A: “Pappus’s theorem for volumes:

Q: Find the volume generated by revolving the area 1 bounded by y -, x = 3, x = 9, and y O about the…

A:

Q: Find the volume of the solid of revolution below. (1,1) 0.5 y = x³ 1 -0.5 X = X 0.5 1.5 2

A: Given: Apply the disk method to find he volume of the solid about the x-axis.…

Q: = 1, 三 a NIU + +

A: Here Let u = x/a, v = y/b , w = z/c Then dx = a du, dy = b dv, dz = c dw So, Required volume V =…

Q: 2. Find the volume of solid generated by revolving te area enclosed by: x=y2+1, x=0, y=0 and y=2…

A: The area enclosed by x=y2+1, x=0, y=0 and y=0 The shaded portion is the required region

Q: . Find the volume bounded by z = 9 –x² – y² and z = 0. Give a numerical %3D answer.

A: Given that the region is bounded by z=9-x2-y2 and z=0. We know that the volume bounded between…

Q: Compute the volume lying inside the sphere x^2+y^2+z^2=21 but outside of x^2+y^2=12…

A: Let E be the solid be described in the question. x=r cos θ,y=r sin θ, z=z, dV=r dz dr dθ So,

Q: For a right circular cylinder, suppose that r= 6 in and H=7 in. Find the exact: Volume

A: Given Radius (r) = 6 in Height (h)=7 in To find Volume of right circular cylinder

Q: Find the volume generated by revolving the area bounded by   xy=4, x=1, x=4 and the x-axis about the…

A:

Q: Find the volume generated by revolving the area bounded by : 2, x = 5, and Ж — x3 + 9x² + 18x y = 0…

A:

Q: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of…

A: There are two Theorem by Pappus 1st for surface area of revolution and 2nd for volume of revolution…

Q: 9. Find the volume generated by revolving the given plane area about the given line using the disc…

A: We are given two regions: (a) y=2x2, y=0, x=0, x=5 about x-axis. (b) x2-y2=16, y=0, x=8 about…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.