Find the area of the region enclosed between y = 3 sin(x) and y = 2 cos(x) from x = 0 tox = 0.5x. Hint: Notice that this region consists of two parts.

Q: Find the area of the region shared by the cardiods r=12(1+cosθ) and r=12(1-cosθ)

A:

Q: Calculate the area of the shaded region, where f(x) = sin(x) and g(x) = cos(x).

A: Given that fx=sin xgx=cos x To find the area of the shaded region of the curves from 0 to 2π The…

Q: Find the area in the first quadrant inside the curve r = 4 + cos 2θ but outside the curve r = 3 cos…

A: Given  The outside the curve r = 4 + cos 2θ but inside the curve r = 3 cos 2θ . Formula for area…

Q: Find the area inside the large loop and outside the small loop of r = 1 + 5 sin(θ)

A: Given, r=1+5sinθ Firstly, sketch the graph of the region to find the area.

Q: Find the area of the region enclosed by one loop of the curve r = 2 sin(50). Also include a sketch…

A:

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Sketch the region enclosed by the given curves. y = 6 cos(7x),    y = 6 sin(14x),    x = 0,    x =…

A:

Q: . Find the area between the curves r = sin0, and r = V3cos0

A: Area of polar curve

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.