7. Rotate the region bound by y = Vx, x = 0, x = 4 and y = 0 around the line x = 10. Find ne volume of this region.

Q: 5. Find the volume generated by revolving the area under the eurve y = e from x = 0 to x = 1 (a)…

A: Given problem is :

Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

A:

Q: If the area bounded by y = x² and y = 2 – x² is revolved about the x – axis and a vertical…

A: We have to find the volume of the solid if the area bounded by y=x2 and y=2-x2 is revolved about the…

Q: 9. Find the volume of the solid whose base is the region enclosed by y = 2 –- x² and the x-axis and…

A:

Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: 20. Find the volume of the region bounded by z = 6x/1+y³+y, z = 0, y = x, y = x/3, and y = 2.

A:

Q: 1. If the region bounded by the two curves is revolved about x = 4, what is the volume of the…

A:

Q: 3. Find the volume of the solid generated when the region enclosed by y = v2x + 8, y = x, x = 0 is…

A: Given

Q: 15 - Which of the following is the volume of the object that occurs when the region bound by the y =…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the y…

Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

Q: 2. Find the volume of the solid generated when the region bounded by y = x? - x and y = x – x² is…

A: For calculating the volume of the solid revolution about particular axis, we will find the original…

Q: 12. Find the volume of the solid that results when the region bound by x 1-y and the y-axis is…

A:

Q: 10. Find the volume of the solid obtained by rotating the region bounded by y = x³. x = 0, and x = 1…

A:

Q: 2.5 Find the volume of the solid of revolution formed by rotating the area under y = 9 – x? over [0,…

A:

Q: Find the volume generated if the area between y = coshx and x from x = 0 to x = 1 is resolved about…

A:

Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: 4. Obtain the volume of the solid that occur when the small side of the circle x +y =2 and the…

A: Graph of the given curves looks like this,

Q: Suppose that RR is the finite region bounded by  y=x, y=x+4, x=0, and x=2. Find the exact value of…

A:

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

A: First we sketch the region using a graphing calculator The shaded region is rotating about the x…

Q: Look for the volume of the solid produced by rotating the region enclosed by about x? - 2kx – 4ky +…

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line…

Q: 1) Calculate the volume of the solid created by rotating the region bounded by y = x² +1 y = -x + 3…

A:

Q: 3. If the region bounded by the curves y =x, y=0, and x =9 is the base of a solid, and cross…

A:

Q: 14 - Which of the following is the volume of the object that occurs when the region bound by the y=…

A: We sketch the region using a graphing calculator  The shaded region will rotate around the x axis

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

A:

Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

A:

Q: 1) Compute the volume of the solid obtained by revolving around the r-axis by 27 (ie. a full…

A: Note: Since, you have asked multiple question, we will solve the first question for you. If you want…

Q: 4. Compute the volume rotating the area shown through one revolution about the x-axis. generated by

A:

Q: 9. Find the volume of the solid obtained by rotating the region bounded by y = Vx. x 0, and x = 4…

A: To find: The volume of the solid obtain by rotating the region bounded by y=x, x=0 and x=4 about the…

Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 4. Set up a (sum of) definite integral(s) that is equal to the volume of the solid whose base is R…

A:

Q: 2. Find the volume of the region bounded by y = x3 and y = x rotated about %3D the x-axis.

A: In this problem we can use washer method to find the volume of the solid of revolution. Washer…

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the xy…

A: We sketch the region using a graphing calculator  The shaded region rotates around the y axis

Q: Find the volume V obtained by revolving the region between y = x2 + 4 and y = 2 about the x-axis for…

A: To find: The volume V obtained by revolving the region between y = x2 + 4 and y = 2 about the x-axis…

Q: 2) Find the volume generated by the area bounded by y = x², y = 4x, revolved about x-axis.

A:

Q: and y=2 8) x = y² +1₁ x = 0, you, The most appropriate method to use to find the volume generated by…

A: The given region is x=y2+1,x=0,y=-1 and y=2. Find the volume generated by revolving the region about…

Q: 4) Find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

A: We find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

Q: 1 3) Consider the region bounded by the graphs of y =-x, y= V4-x , and y=0. 3 c) If this region is…

A:

Q: (4) Find the volume of the solid obtained by rotating the region bounded by y y=√x about the y = 1.…

A:

Q: 1- Find the volume of the solid obtained by rotating the region bounded by the curve y = 4 - r and…

A: The volume of the solid of the revolution of the curve y=f(x) obtained is  Volume=∫abA(x)dx  or…

Q: 9) Find the volume of the region bounded by y = x + 1 x +1' Y = 0, x = 0, and у %3D0, х%3D x = 4…

A: The formula for the washer method around the x-axis is V=π∫abf(x)2-g(x)2dx where f(x) is the top…

Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

A:

Q: 17. Find the volume of the solid that results when the region enclosed by y = √x, y = 0, and 2 = 9…

A: According to our guidelines, we can answer only the first problem or first three subparts of a…

Q: 46. Find the volume of the solid produced by rotating the region enclosed line y = -1 that is…

A:

Q: 3. Find the volume of the region common to the interiors of cylinders a? + y² = 1 and r? + z2 = 1

A:

Q: 2. Find the volume of the region common to the cylinders r2 + y² = 9 and z2 + z² = 9.

A: USING  FORMULA VOLUME =8∫∫∫dxdydz

Q: 1. Show by integration that the volume V of a right circular cylinder with base radius r and height…

A: We’ll answer the first part of this question. since due to complexity. Please submit the question…

Q: 5. Find the volume generated by the areas bounded by the straight line y = x, between y = 0 and x =…

A:

Q: 6) Use the washer method to find the volume of the solid generated by revolving the region y = x² +1…

A: We first sketch the region using a graphing calculator. From the graph, we see that x is from 0 to…

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.