Creating the Midpoint Sum Suppose that an object moving along a straight line path has its velocity in feet per second at time t in seconds given by v(t) =(- 3)2 + 2. We will approximate this area by creating the left-hand sum by constructing four rectangles to approximation the bo aron
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.
![Creating the Midpoint Sum
Suppose that an object moving along a straight line
path has its velocity in feet per second at time t in
seconds given by v(t) -3(1- 3)2 + 2.
We will approximate this area by creating the left-hand
sum by constructing four rectangles to approximation
the area.
To create the midpoint sum you need to evaluate the
function at each of the midpoints of the subintervals.
On the graph, sketch the four rectangles whose areas
you need to find. The enter the midpoints of each
interval below. Once your table is correct, the rest of the
problem will be revealed.
Interval [a,b)
Midpoint
Got it?
Keep trying!
[.]
Keep trying!
-2
[.]
Keep trying!
[]
Keep trying!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7b7073d-4cc9-48c4-8921-61402f300ff6%2F56dfe395-4801-4b17-80a6-e1096af74667%2Fidy7sqa_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
