Using the expression A = Sa (xR -XL) dy, find the area enclosed by the parabola 2XL +6 and the line y= -1+ X R, where a = -2 and b=4 %3D

Q: Q5 Find the area of the portion of the surface inside the sphere 2x = y² + 2² x² + y² +2²=4.

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Q: Convert this into a quadratic in standard form. State a, b, and c for your solution. 3(x- 2) +1 = 28…

A: Using standard form of quadratic equations,

Q: III. Evaluate 4 - x -dx. V16 – x2

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Q: (2) Determine the intersection points of y=-x² +9 and y = 5. Then find the area bounded by this…

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Q: Find the area under the curve of the parabola y = x? - 2x + 2, above the x-axis and between x=0 and…

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Q: area bounded by f(x) = 9x² – 2x + 1, the x-axis, x = -2 and x = 1

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Q: Use inscribed and circumscribed rectangles to find the area of the region to the right of the line x…

A: Concept: the area between the region y=f(x) and ==g(x) on the interval [a, b] Let us assume that…

Q: Find the area between the curves: y = x³15x² + 50x and y = x³ + 15x² - 50x

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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.