Q4. Graph and set up The integral for The area, DO NOT EVALUATE INTEGRALS. Ca) Inside r=2 Cos (50) A= S DdO Answer !' Cb) laside both r= It sine) and r= A=S

Q: Graph of the function y = cos 2x What is the area of the region bounded by the x = 15°, x = 45°…

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Q: If sets A and B are disjoint and |A|=7and |B|=8, what is |A∪B|+|A∩B|?

A: Here given that sets A and B are disjoint and A=7 and B=8 .We have to find A∪B+A∩B.

Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

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Q: Find the area enclosed by the curve r=9+sin(4theta)

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Q: Find the area

A: Step 1: Step 2: Step 3:na Step 4:

Q: For each problem below write an expression in the form ax + by + cz in the first blank, then choose…

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Q: Find the area of the region outside r = 6+ 6 sin 0 , but inside r = 18 sin 0.

A: The given curves are,r=6+6sinθ=r1(let)and r=18sinθ=r2(let) We need to find the area of the sketched…

Q: Find the area enclosed by the curve r V6(1 – sin®). %3D

A: First we will plot the curve and and using Double integration we will find area bounded

Q: Q-Find the area of the region that outside r= 2 sin (e) and inside r= (1+cos e)? %3D

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Q: Find the area under the cosine curve from 0 to

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Q: find the integral by polar coordinate SS (se'ty') dydx, whore

A: The solution is given as

Q: Integrate, if the integral exists Sa° (r° – 7)*dz

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Q: Find the area inside r = 1 + 2 cos 0 and outside r = 2.

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Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: (3X dx =? Sinmply

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Q: Suppose that a population grows according to a logistic model with carrying capacity 5700 and k =…

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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.