1. The graph of f (x) = 8-x3 and line /which is tangent to f at x = 1 is shown in the figure to the right. Ris the shaded region between f and / and the y axis while S is the shaded region between f and / and the x axis. 1.1 1.2 *Unsaved R. (1,7) (a) Find the total area of the regions R+ S. Line 1 ik)-8-x (b) Region R is the base of a solid. For this solid, each cross-section perpendicular to the x axis is a semi-circle. Find the volume of this solid. (c) Region S is rotated about the y axis to form a solid. Find the volume of this solid.

Q: 1) Determine the area of the region bounded by the graph of the function and the tangent line to the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: If RR is the region bounded by the graphs of the functions. f(x)=6x−7.25    and    g(x)=−8x−8.75…

A: Given: f(x)=6x-7.25 g(x)=-8x-8.75

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A: You have posted the multiple question. I am answering the first one. Please post the question again…

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: 12) Find the area of the region between the curve y = 22-X and the interval 0 < x < 2 on the х-ахis.

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Q: Sketch the graph of the function. Ax) = xe2 y 10아 5아 -3 -2 3 - 50- -100- y y 10아 100- 100- 5아 5아 5아…

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Q: 7. Find the area bounded by the two curves, f (x) = x and f (x) = x + 2 between x-0 and x=2. Hint:…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 26. Given two curves as follow: a) b) y = -x² - 1 y=x²+x=2 Sketch and shade the region bounded by…

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Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

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Q: 3. To the right is a plot of the line of equality and the Lorenz curve for Poland in the year 2018.…

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Q: Can i get help step by step with this problem please

A: It is given that f(x) = 5x2, x0 = 0 and xn=2.(i)

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A: Given:A parallelogram bounded by the y-axis, the line x = 3, the line f (x) = 1 + 2x, and the line…

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A: As per guidelines, I can answer maximum three subparts if a question. Since you have asked fot…

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Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

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Q: 4 Find the area bounded by the curve y = the x - axis, and the vertical lines x = -2 x²+4 and x = 2.

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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.