Math problem

Elementary Calculus Final Report Activity brief

BCO116 Elementary Calculus Online campus

Professor: Paulo Azevedo | [email protected]

Description Written report describing the various steps of the required calculations. The questions are shown below.

Format Written report:

 DOC, DOCX or PDF file  No specific formatting or styling rules.  No need for references.

You may paste scanned images or photographs from your handwritten work – a few sentences may have to be typed for the submission to be accepted.

Goal(s) Test the students’ understanding of the Elementary Calculus topics covered from Week 5 to Week 8, namely integration and calculation of areas using integration.

Due date Date: Monday, July 19, 2021 Time: 14:00 CEST

Weight towards final grade

This activity has a weight of 60% towards the final grade.

Learning outcomes

6. understand basic integration techniques to solve simple differential equations.

7. understand and locate the concepts of limits, derivatives, and integrals within the business context to illustrate problems involving functions and interpret the results in that context.

Assessment criteria

See the rubric below.

 Question 1 - 10%;

 Question 2 - 20%;

 Question 3 - 20%;

 Question 4 - 25%;

 Question 5 - 25%;

Questions

Calculate the following areas:

1. Limited by the function y=−x 2 , the x -axis and the points x = -2 and x = 2. (10 points)

2. Limited by the function y=6xe x

2

, the x-axis and the points x = 0 and x = 2. (20 points)

3. Limited by the function y= 3 x

2 −3

x 3 −3x

the x-axis and the points x = 2 and x = 4.

(Tip: You will need a scientific calculator for the last step) (20 points)

4. Limited by the function y=cos 3 x, the x-axis and the points x = π 12

( 15º )and x = π 6

( 30º ).

(Tip : you may need a scientific calculator for finding some trigonometric values) (25 points)

5. Limited by the function y=xsinx, the x-axis and the points x = π 6

( 30º )and x = π 3

( 60º ).

(Tip : you may need a scientific calculator for finding some trigonometric values) (25 points)

Rubric

Task Between 90% and 100% Between 80% and 90% Between 60% and 80% Between 30% and 60% Between 0% and 30%

Calculation Result and process are correct, and answer is well explained (process is detailed).

Minor details may cause deduction of points.

Minor errors leading to wrong result, but explanation is clear and process is generally correct.

Some important errors revealing some confusion, but partially correct process.

Seemingly correct process and correct result, but no adequate explanation is provided

Important errors revealing significant misunderstanding of relevant concepts, but the process is not entirely wrong.

Wrong result, lacking any coherent explanation.