Q. Let (X, B(R), µ) be a Borel measure space. If An B = 0, BnC = 4 µ(ANC) = 0 Determine u(AUBUC).

Q: Assume that D is bounded by the lines y = x +1, y = x, x = 0, and æ = 1. Calculate: S Sp e22 dA =…

A: Given : y=x , y=x+1 x=0, x=1 To find integration of e²² da

Q: 28, g6) = 2x2 [,3],8 reclanyles

A:

Q: What relationship do you see between the segments of the median that are formed by the centroid?

A:

Q: Find the exact area of the surface obtained by rotating the curre around the x - as is 1 16-x1 g= +…

A: Given that , y=6-x , 4≤x≤6 find the area of the surface obtained by rotating the curve around the…

Q: a. Using three approximating rectangles and midpoints, find the approximate area under the curve of:…

A: The given function  , The midpoint rule

Q: Find the boundary of Ei= { ERIM, MEN } R²im,

A:

Q: Find the average value of the distance from a point in a sphere of radius R to the center of the…

A:

Q: A piece of wire 150 cm long is cut into two parts. A square is made from the first piece, and a…

A:

Q: 1)Find the area bounded by the given curves: a)y = 6x2 and y = 24   b)y = 3x2 − 12 and y = 0

A: The given function are y=6x2 and y=24. The area bounded by the given curves as shown below:

Q: 11. Find the area of the largest rectangle that fits into the triangle with slides x=0, y=0,…

A: We have to maximize the area of the rectangle which fits inside the triangle. For this differentiate…

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.