The region shown below is bounded by the curve y = 2x3 and the lines x = 8 and y = 3.

Q: Q3:B/ Find the areas of the regions enclosed by the line and the curve y = x* – 4x? + 4 and y = x?

A:

Q: Consider the area bounded by the curves y = 4x³ - x² - 14x and y = x²+2x. Where do the curves…

A: Step 1:Step 2:I hope it is clear if there is any doubt, please ask in clarification section.

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: over the triangular region Cut from the * quadrant by the line x+y =1.

A:

Q: y = 9 - x² and y = x + 3 is 125 6 square units

A:

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2+2t, z = 3+ t.

A: Find the distance from the point (2, 2, 3) to the line x= 0, y=2+2t, z=3+t.

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2 + 2t, z = 3 + t.

A: Given point (2,2,3)and line is x=0 , y=2+2t ,z=3+t.

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.