Suppose water flows into and out of a bay and the rate of this flow is given by the function f (t) . Note, if water is flowing in f > 0, and if water flows out f <0. A. Write an expression for the net change in the amount of water during the interval (t1, t2]- B. Write an expression for the amount of water that moved during the interval t1, t2], regardless if the water was flowing in or out. Both of the expressions above will involve integrals and wilI be written in terms of the functions and variables given above.
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.
![Suppose water flows into and out of a bay and the rate of this flow is given by
the function f (t) . Note, if water is flowing in f > 0, and if water flows out
f <0.
A. Write an expression for the net change in the amount of water during the
interval t1, t2].
B. Write an expression for the amount of water that moved during the
interval t1, t2), regardless if the water was flowing in or out.
Both of the expressions above will involve integrals and will be written in
terms of the functions and variables given above.
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