a) x2 y 1,z = 4 - x2-y2, z = 0 b) x2 y2 1,x2 z2 = 1

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 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: Calculate the volume of one of the wedge-like objects formed by cutting the cylinder x²+9y²=a² with…

A:

Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

A:

Q: By using either a double or triple integral, find the volume of the tetrahedron with vertices…

A: To determine :- The volume of the tetrahedron with vertices 0,0,0 , 1,0,0 , 0,1,0 , 0,0,1.

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

A:

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4 – x2 – y² , y =…

A: The volume of the solid in first quadrant is given by: V=∫ab∫cdf(z)dydx Now, find the range of the…

Q: find The volume of Ihe solid generated by revolving each vegion enclosed by he triangle wilh…

A:

Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

A:

Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

A:

Q: Find the volume of the and the coordinate planes. tetrahedron bounded by 2x-y +z = 4

A:

Q: Use the Theorem of Pappus to find the exact volume of a general cone created vertices (0, 0), (1,0),…

A:

Q: Find the volume under the plane z= 2x + y and over the rectangle R = {(x, y) : 3<x< 5,1< y< 2

A: Given Rectangle  R=x,y:3≤x≤5,1≤y≤2

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 of the solid generated by revolving the region bo x-axis. 16) y = √ , y=0, x= 1, x =…

A: Introduction: To determine the volume of specific solids, one can utilize the disc method, an…

Q: The volume of an object determined by the two surfaces is z=(x^2+y^2)-2 , z=8-3(x^2+y^2)

A: Let's find.

Q: By using either a double or triple integral, find the volume of the tetrahedron with vertices…

A:

Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

A:

Q: (c) Semicircles (d) Isosceles right triangles y 2)

A: Part C) To find the volume of the solid whose bases are bounded by the circle x2+y2=4,  And the…

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

A:

Q: By using shell method, find the following volume a. y = (x-3)2 and line y = -2x + 6 about x axis

A: Two functions are given by y=x-32 and y=-2x+6. The objective is to find the volume bounded by the…

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

A:

Q: Find the volumes of the solids whose bases are bounded by the graphs of y = x + 1 and y = x² - 1,…

A: AREA OF SQUARE=side×side Area of rectangle=Length×breadth

Q: Let a and b two real numbers such that a < b. A region R is bounded by a curve C and two different…

A: Given: A region R is bounded by a curve C and two parallel lines to x-axis and C does not cut y-axis…

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A: Sphere was cut at height h, radius of the circle at intersection of 2 cuts is r2-h2. Similarly…

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4-x2-y2, y= 2-2x2,…

A:

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 of the tetrahedron in the first octant that is bounded by the three coordinate…

A: The objective is to find the volume of the tetrahedron in the first octant that is bounded by the…

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

A: Given

Q: 4. Find the volume and centroid generated by revolving the given plane area about y=6x-x^2,…

A: Given:    y=6x-x2   y=x2-2x     y = -1

Q: Find the volumes of the solids formed when the region bounded by y = 0 and y = 1/x, between x = 1…

A:

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: = 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: Find the volume of the solid bounded by the graphs of the equations: z = 3x + 3y?, x - y+1 = 0, 3x +…

A: This question is about application of intergal calculas

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: Please see the attachment

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum , when it…

A:

Q: FiNd the volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF the…

A:

Q: Find the volume of the region bounded above by the elliptical paraboloid z = 16 - x2 - y2 and below…

A:

Q: Find the volume V which lies inside the sphere x2+y2+(z−5)2=25 and outside the sphere x2+y2+z2=4.…

A:

Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

A:

Q: find volume 31. The region in the first octant bounded by the coordinate planes, the plane x + y =…

A:

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: Show that the surface area of a closed cuboid with square base and given volume is minimum, when it…

A: Let the length be x , breadth be x and height be y of a closed cuboid with a square base.So Volume…

Q: Find the volume generated by y = x^2, x=0 and y = 4 rotated about the y axis. with drawing please.

A:

Q: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…

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.