*label*Mathematics

### Question Description

## Discussion-Based Assessment Instructions

For this assignment, you will be completing a Discussion-Based Assessment on material covered in the course. All students must complete at least one Discussion-Based Assessment in each segment of the course.

## Part 1:

Once you have completed the lesson material in this module, complete and submit the assigned problems to your instructor.

## Discussion-Based Assessment Assigned Problems SHOW ALL WORK

- Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.

- Explain, using a graph of f(x), what the Riemann sum in Question #1 represents.

- Express the given integral as the limit of a Riemann sum but do not evaluate: .

- Use the Fundamental Theorem to evaluate .

(Your answer must include the antiderivative.)

- Use a graph of the function to explain the geometric meaning of the value of the integral.

(Your answer must include the antiderivative.)

## Part 2:

Answer the following questions and submit in order to receive credit for completing the assessment:

Over the course of this unit, what concept did you find the most challenging? What did you do to clarify this concept and further your learning? Please explain the concept and give at least one real world example that demonstrates the concept that you have selected.

Your response must be at least three paragraphs.

## Tutor Answer

Hello, I'm done, all parts 1 and 2 are fully answered as per the instructions.

Running Head: DISCUSSION-BASED ASSESSMENT

Discussion-Based Assessment

Name

Professor

Author

Institution

Course

Date

1

DISCUSSION-BASED ASSESSMENT

2

PART 1

Solution

▲x= (b-a)/n = (3-0)/6 = 0.5

Right endpoints

Therefore, Riemann equation when expressed to three decimal places will be equivalent to,

= 3.938

DISCUSSION-BASED ASSESSMENT

3

DISCUSSION-BASED ASSES...

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