State the formula for the Area of the sector bounded by a polar curve r = f (θ ) and two rays θ = α and θ = β.

Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

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Q: Calculate the area of the circle r = 3 sin θ bounded by the rays θ = π/3 and θ = 2π/3.

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Q: Graph the curve x = 2 cos(theta) − cos(2theta),     y = 2 sin(theta) − sin(2theta) If this curve is…

A: Given parametric curves x=2cosθ-cos2θ,  y=2sinθ-sin2θ. The objective is to graph the curve and find…

Q: What is the formula for the derivative for dy/dx for a polar curve r=f(theta)?

A: Given that

Q: Locate the center of the curve r = 4(sinθ + cosθ)

A: NOTE: Refresh your page if you can't see any equations. . the given curve is ...............(1)

Q: Given the polar function r = f(theta) = 4sin(2theta) Find the average rate of change of f between…

A: Step 1:

Q: Consider the polar curve r = 02. dr dy (a) Find and OP .OP dr in terms of 0. (b) Find the slope of…

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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.