Areas of regions Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the inner loop of r = cos θ - 1/2

Q: The limaçon family The equations r = a + b cos θ and r = a + b sin θ describe curves known as…

A:

Q: Use a graphing utility to graph the polar equation. Inner loop of r 3+6 cos(8)

A: Clearly we can see that r = 0 at cos(theta) = (-1/2). Hence the inner loop will be at the right…

Q: The region inside r = Vcos(0) and inside r= in the first quadrant Ans: 3 V2

A: Hi! You have posted multiple questions. As per norms, we will be answering the first question as…

Q: . Monthly Temperature The data on the next page representthe average monthly temperatures for…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The curve shown in the figure is the astroid x = a cos³(8), y = a sin³(8). -a YA a 0 -a a x Find the…

A:

Q: Polar equation f(theta)=1+2sin(theta) A. sketch the graph B. Fins area bound by the inner loop of…

A:

Q: Find the arc length

A: Given,            r=a(1-cosθ).

Q: Use a graphing utility to graph the polar equations. Find the area of the given region analytically.…

A: We have given the polar equation;

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.