Q1:By triple integration, determine the volume enclosed by two surfaces y =x 2+z2, y =-x2-z 2.

Q: Find the volume of the solid that results when the region enclosed by y = e2", y = 0, x = 0, x = ln…

A: Topic:- application of integration

Q: Q4 Calculate the volume of the solid obtained by rotating the region bounded by the parabola 4py =…

A:

Q: Q1/ Find the volume of the solid generated by revolving the region bounded by y = Vcos x, y = 0 & 0s…

A: To findVolume of solid generated by revolving the region bounded by y=cosx  , y=0  & 0≤x≤π2…

Q: Q3/ Find the volume of the solid generated by revolving the region bounded by y = 3/(2√x), y = 0 &…

A: We have to find the volume of the solid generated by revolving the region bounded by y=32x, y=0 and…

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: Use a double integral to find the volume of the indicated solid. 8 z = 8- X- y 6. 4 1 2 4 V 3 y=4 4…

A:

Q: Q4) Fid the volume of the solid generated by revolving the region between the curve y = x + 1 and…

A:

Q: The area bounded by y = x² and y = 2 – x² is revolved about the x-axis. Find the volume of the solid…

A: We have to find volume of solid revolution.

Q: The volume of the solid obtained by rotating the region enclosed by 5x y = e° + 5, y = 0, x = 0, x =…

A:

Q: Q.5 Find the volume of the solid whose base is the region enclosed between the curve x=1-y and the…

A:

Q: Set the limits of integration for finding the volume of the solid inside the sphere x2 + y2 + z2 =…

A: Given: Equation of the sphere: x2+ y2+ z2=16  Equation of cylinder: x2+y2=4 To Find: We have to set…

Q: Q4/ Find the volume of the solid generated by revolving the region in the first quadrant bounded by…

A:

Q: The area enclosed between the two curves x² = 2y and y² = 2x is rotated about the x- axis. Determine…

A:

Q: The area defined by the curves: y= 10/ square root (x2+1)    ;     x=1, x=4, y=1 is rotated around…

A:

Q: Use a double integral to find the volume of the indicated solid. 8. X+y+Z =8 8. 8.

A: Given:       x+y+z=8 To find:          Volume of the indicated solid

Q: Find the volume of the solid using integration on the interval [0,2]. Assume the units are feet. 4+…

A: given base=x height=x2

Q: Use double integration to find the volume of the solid. ... 3x + 2y + 4z = 12

A:

Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

Q: The volume of the solid obtained by rotating the region enclosed by y = eSz + 2, y = 0, T = 0, I=0.4…

A:

Q: So, the volume of the solid of revolution is Volume = V = t (25 - x2)2 dx. To find the volume,…

A: A step of a problem is given. The sub steps of the given steps is to be completed. The solution is…

Q: Use triple integration to find the volume of the solid bounded above by z = 4 – y? and on the sides…

A:

Q: The volume of the solid obtained by rotating the region enclosed by y = x", y = 6x, about the line y…

A: First sketch the curves then use method of disc to get the volume of solid obtained.

Q: The solid enclosed by y = x, z = 0, and x +z= 1.

A: Let's find .

Q: Q2/ Find the volume of the solid generated by revolving the region bounded by y = x² +1, y= x+3…

A: According to bartleby guidelines i can do only 1 question please reupload 2nd qstn

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 6x^5 on the…

A: Given fx=6x5 rotated about x axis in the interval x=-2 , x=+2Find volume generated .

Q: In the given question , find the volume of the solid generated by revolving the region bounded by…

A:

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

Q: Q2/ Find the volume of the solid generated by revolving the region bounded by y = x² +1, y = x+ 3…

A: Given Equation of parabola y=x2+1. Equation of line y=x+3.

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y2 = 4x, about the…

A: Here we solve the integral problem.

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 7x^5 on the…

A:

Q: 2. Find the volume of the solid that results when the region enclosed by y= x? and y = 12 –x is…

A:

Q: Use a double integral to find the volume of the indicated solid. z = 8-2y 2 y=2

A: The expression for the volume as double integral is: V=∬zdydx From the given equation: z=8-2y

Q: Q1/ Find the volume of the solid generated by revolving the region bounded by y = vcos x, y = 0 &…

A:

Q: Find the volume of the solid of revolution generated by revolving y = 9-x from x= - 3 to x= 3 about…

A: Given f(x)= 9-x2    where -3≤x≤3 To find the volume of the solid of revolution here use The Disc…

Q: Use a double integral to find the volume of the indicated solid. 8 z = 8- X- y 4 21 4. y-4 4. y=x 3.…

A:

Q: 7. Find the volume of the solid under the surface 1 = 3x+ 2y? above 1 < x < 3, 0 < y < 6 using a…

A: Introduction: We know that the volume under the curve z=f(x,y) and over the region R is given by the…

Q: 1. Use disk or washer methods: Determine the volume of solid endosed by y = vx- 5 and x 14, about:…

A: As per our guidelines, we are supposed to solve only first question with first three subparts.…

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: Given that , fx=x2+1 and gx=-x2+2x+5 find the volume of solid generated by revolving the region…

Q: So, the volume of the solid of revolution is Volume = V3 = (9 - x)2 dx. To find the volume,…

A:

Q: Use a double integral to find the volume of the indicated solid. 16 15 z 16- X-y 14

A: We are given the following. So, we have 0≤z≤16-x-y,  x≤y≤8, 0≤x≤8.

Q: What is the volume, in cubic units, of the solid obtained by rotating the region bounded by y = 4x-…

A:

Q: Q2/ Find the volume of the solid generated by revolving the region bounded by y = x² +1, y=x+3 about…

A: Given y=x2+1y=x+3

Q: The volume for solid of revolution between the curves y = v(49- x^2) and y = 0 around the x - axis…

A: Let's find volume of solid of given curves.

Q: The region bounded by f(x) = - 2x² + 8x + 24, x = 0, and y = 0 is rotated about the y-axis. Find the…

A: Introduction: When the cross-sectional area is perpendicular to the axis of revolution and the axis…

Q: Find the volume x=y-y2; x=0 revolving at y-axis

A: Given problem:- Find the volume x=y-y2 ; x=0 revolving at y-axis

Q: The area bounded by y=3x and 2y=x is revolved about the x-axis. Using cylindrical shell method, set…

A:

Q: Use integration to find the volume of the solid that lies within the cylinder + y= 4, below the cone…

A: We will find out the required volume.

Q: Find the volume of the solid bounded by the cylinders x2 + y2 = 4r2, y2 + z2 = 4r2.

A: We know that : Volume under the surface z = f(x, y) and above the region D in x-y plane is given by

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.