2. a) Sketch the region enclosed by the curves y=-x² +3x and y= x². Hence, find the area of the region. b) Find the volume of the solid generated by the curve f(x)=4- cos x revolved 360° about the x-axis in the interval [0, 27]

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Q: In Exercises 17–20, find the volume of the solid generated by revolv- ing the shaded region about…

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

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Q: 5.5 Find the volume of the solid bounded above by the graph of f(x, y) = xy sin(x²y) and below by…

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Q: 24 22. Find the volume generated by revolving about Ox the area bounded by the Ans. ra³. hyperbola…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

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Q: and the y-axis. 2. Evaluate , 5x³ cos(y³) dA, where D is the region bounded by y = 2, y =:

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: Define R as the region bounded by the graphs of f(x)=x2 +4x+5, x=−3, x=0, and the x-axis. Using the…

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A: Solution :- As per guidelines . I do first only.

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.