Consider the region R bounded by the graphs of y = ƒ(x) > 0, x = a > 0, x = b > a, and y = 0 . If the volume of the solid formed by revolving R about the x-axis is 4p, and the volume of the solid formed by revolving R about the line y = -1 is 8p, find the area of R.

Q: Find the area bounded by the following curve and line: y=4/x , y²-4y+2x=5 and the line y=4

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Q: Find the area bounded by the curve x y2 +2y and the line z = 3. %3D

A: Given :                curve x = y2 + 2y and the line is x = 3 To find :               The area…

Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: Use Taylor expansion with the Lagrange Remainder, prove the following inequalities 1. x * 0. 2. x –…

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Q: Determine the area of the region enclosed by the curves y=1/x, y=1/x2, and x=9.

A:

Q: Find the area of the region lying between the x-axis and the curve In(82) – 1 to the right of the…

A: Given curve is: y=ln8x-1x2 The area of region of the curve lying between x-axis and right of the…

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

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.