Estimate the volume of the solid that lies under the surface z = f(x, y) = x2 + y? and above the rectangular region R = [0, 2] × [0, 2]. Divide Rinto four squares with m = n = 2, and choose the sample point as the midpoint of each square.

Q: Find the area of the shaded region: 1. y=x+4 (3,7) (-2, y=r-2

A: Area between the curves

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: Find the surface area in r(r,0)=(rcos)i + (rsin0) j+0k, 0≤0≤2ñ, 0≤r≤1. the accompanying (1, 0, 2)…

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

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

A:

Q: Consider the region bounded by y = x² and y = 8. Find the number b so the line y = b divides this…

A:

Q: (14, 2) (3714, 2) y = csc2x 4 4

A:

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

A:

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: Given that  Plane x+7y+10z=70  To find the largest volume

Q: An office allots 85,000 a month for operational expenses such that 3/5 is allotted to the basic…

A: In this question, Given that office allots 85,000 a month for operational expenses  35 is allotted…

Q: Find the area bounded by the lines: X = x =/y+3.x = y+3 %3D 4/9 9 square units $/s square units 4/3…

A: Area between curves

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.