|Find the volume of the solid below The solid S whose base is the region R enclosed by the curve y = -(x - 2)2 + 1 and the x-axis, and whose cross-sections perpendicular to the x-axis are rectangles whose height is twice the length of the basis

Q: Determine the centroid of a cross section with an isosceles right triangle of base 9 cm, a…

A: Determine the centroid of a cross section with an isosceles right triangle of base 9 cm, a…

Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Verify by integration that the Xbar location of the centroid of a quarter circle is (4r/3 pi)

A:

Q: A thin metal plate of uniform density covers the area between the curves y = 2+ 6x – x² and y = 2 –…

A:

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: Find the center of mass of a thin plate of constant density 8 covering the given region. The region…

A:

Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line 5y = 0.…

A:

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is  fx,y=x2+y2-2x-2y where bounded region is  x2+y2≤8.

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the volume of the solid of revolution generated by the flat region under the curve obtained by…

A:

Q: Find the area of the surface generated when the curve: =y=+on [1,2] is rotated about the x-axis. 2 0…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

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.