Let R and S in the figure to the right be defined as follows: Ris the region in the first and second quadrants bounded by the graphs of y= 3- and y-2". S is the shaded region in the first quadrant bounded by the two graphs, the x-axis, and the y-axis. a. Find the area of region S. b. Find the volume of the solid generated when R is rotated about the horizontal line y = -1. c. The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a semi-circle whose diameter lies on the base of the solid. Find the volume of this solid.

Q: 2. Graph and shade the region enclosed by the curves y= (x – 3) and y = x . Find the volume of the…

A:

Q: 1. Find the total area enclosed between the curves y 27² and y = 1¹ - 21². It is usually a good idea…

A: Given, y=2x2, y=x4-2x2

Q: Calculate the surface area of the region where o=90°, 4<R<10 and 21°<e<53".

A:

Q: Find the area of the plane region bounded by the curves y = Vx - 1, y = 3, the x-axis, and the…

A: Region bounded be the curves is given, we need to find the area of the region. Firstly,  we'll draw…

Q: 02. Find the area of the region R enclosed by the parabola y = 4-x and the line y = 3x. Sketch the…

A:

Q: 3) Find the volume of the first quadrant region bounded by y = x² , the y-axis and y = 4 rotated…

A: Please refer the attached image for complete solution.

Q: 1. Graph and shade the region enclosed by the curves x=(y-2) and y= x . Find the volume of the solid…

A:

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: the area is given by A=∫ab|fx-gx|dx here we have fx=7x g(x)=0 a=0, b=16

Q: 8. The region enclosed by the circle with equation + y² = 5 and the +². line x = 1, shown shaded in…

A:

Q: 2. Sketch the graphs of y = x² - 6x + 12, x = 5, x-axis and y-axis. Shade the region bounded by the…

A: The given equation of the curve is: and

Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

A:

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.