 # Definite Integrals (480 words)

Subject Mathematics Calculus

## Question

On clean paper, legibly print or write, in clear and concise English, a description of the development of the definite integral over a segment [a, b]. You may use a specific function or a general function, f. Your description should be logically organized, didactic, and sufficient that any individual with pre-calculus training could follow it (you do not have to explain what a derivative is). It should also include the following:

* a basic statement of the problem (curve defined by y = f(x) on an interval [a, b];
* a list of conditions necessary for the Riemann integral to exist;
* an explanation of the role that partitions, minimums or maximums and limits play in the integral;
* the role that the fundamental theorem of calculus plays in evaluating definite integrals.

Note that you can write on the Riemann integral or the Darboux integral (whichever one you are more familiar with).

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

To evaluate these integrals, the fundamental theorem in calculus must be used. The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral. It expresses that the integral of a function F is equal to the function itself plus an arbitrary constant. This constant can be eliminated by substituting the upper and lower limit given in the definite integral. Thus, the limits of a given integral play an important role, for it determines the value of the integral of the function, which represents the area under the curve....

This is only a preview of the solution. Please use the purchase button to see the entire solution

## Related Homework Solutions

Solar Power Equations \$3.00
Solar Power
Mathematics
Equations
Kilowatt-Hours
United States
Energy
Solar Cells
Sun Rays
Panels
Roofs
Calculus
Optimization Problem - Least square \$25.00
Least
Square
Linear
Fit
Optimization
Integral
Matlab
Mathematics
Calculus
Approximation
Linear
Fit
Calculus Questions \$35.00
Calculus
Mathematics
Derivative
Rules
Integral
Antiderivative
Function
Method
Vectors And Planes \$5.00
Mathematics
Calculus
Vectors
Planes
Equations
Algebra Techniques
Dot Product
Perpendicularity
Variables
Equalities
Justification
Evaluating An Integral \$5.00
Mathematics
Integrals
Calculus
Evaluation
Substitution
Expressions
Trigonometry
Constants
Derivatives
Variables
Live Chats