Express by repeated integrals, the volume of the solid bounded above by the plane 2r+ 2y- +130, on the sides by the planes y=x, x=2, y = 0, and below by ==0,

Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

A: We want to find the area bounded by the parabola y2 = 9x and the line y = 3x about the y-axis.

Q: The base of a solid is the region in the first quadrant bounded by the line y = -1/2x + 2 and the…

A: At any point x calculate the area of cross section and integrate it over the interval.

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Find the surface area of the portion of the half ball with radius which cuts off by the cylinder x2…

A: Concept: The surface area of the half ball is given by: A=∬1+∂z∂y2+∂z∂x2dA Where ∂z∂y, ∂z∂x is the…

Q: The area bounded by the parabola y² + x - 2y = 1, the x — axis, and the line x = 2 revolves about…

A:

Q: Problem 4. Suppose that la b C d e f= 2. h i Compute 3g |2а + d 2b +е 2с + f - a 3h - b Зі — с a C

A: Given abcdefghi = 2

Q: Find the volume of the solid bounded by surfaces z = /9-x2 - y2 , and z = /25 - x2 - y? and the…

A:

Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.

Q: The base of a sand pile covers the region in the xy-plane that is bounded by the parabola x2 + y = 6…

A:

Q: Find the volume V of the region appearing between the two surfaces z = x² + y² and z = 8 - x² - y².…

A:

Q: Find the area of the plane x−2y+5z=13 cut out by the cylinder x^2+y^2=9

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.