Read these instructions carefully

• The presentation of your answers matters a lot – you must explain what you are doing and you must use proper mathematical notation (as used in texts, notes etc). Just writing an answer without working is not enough.

Guidelines for submitted work

• This is an academic assignment so it must be referenced. Include a Reference list at the end of your assignment. You must cite all the different authors from different sources (books, journals, electronic). Please do not use Wikipedia or other such non-refereed sources.

• Start each new question on a new page.

• Conduct a spell check yourself and ensure you have a critical friend read and comment on your English usage, grammar, punctuation and other technical issues.

• Please use Microsoft Word Equation to express any mathematical formulas needed, and Microsoft Word to write the assignment or similar software.

• You may use graphical or drawing software to show your graphs.

• Please use size 12 font for any written work.

• Leave a wide margin on the left for feedback comments from your teachers.

What is plagiarism

Plagiarism is when you copy someone else’s answers. Even if you make slight changes in symbols it is still plagiarism. Plagiarism is cheating and is wrong. If it is detected all the people whose answers are extremely similar will get zero marks for the questions involved.

It is a good idea to discuss problems with other people. It is often helpful to work in study groups, but you must write up your answers by yourself and your examples must be unique. Any similarities identified with TURNITIN will be investigated and penalties will be applied .

Integration Assignment

You have been hired to write an introduction to the section on Integration for the Project

“Mathematics 1B Text Book”.

AVOID THE USE OF CALCULATORS AS MUCH AS POSSIBLE, THAT IS, USE NUMBERS THAT ARE SMALL AND EASY TO DO CALCULATIONS WITH

MANUALLY.

QUESTION 1 – 30 marks

Give a brief account of the history of integration. Give answers to at least these questions: Who invented it? When? What were they solving? How did the theorems of calculus solve their problem? How many theorems of calculus are there? You must research this and it must be fully referenced.

QUESTION 2 – 50 marks

Choose any 3D irregular shape you like, (eg your backpack, your shoe) and explain how you would calculate its surface area and its volume based on your explanation of the theorems of calculus in question 1. Make sure you include clear drawings of this shape (you may include pictures too), make sure your explanations are clear and based on integration and geometry. Use simple values to make these calculations and avoid the use of calculators as much as possible. You should not need any references for this section but if you borrow any material from anyone, please reference it appropriately.

QUESTION 3 – 20 marks

Explain one of the advanced methods for solving indefinite integrals analytically. Choose between: completing the square, partial fraction decomposition and integration by parts. Use your own examples in your explanation, that is, choose your own values for “your” functions. Make sure you show the step-by-step calculations and you explain them thoroughly. As with the previous question, your examples should be your own but the theoretical part of your question must be fully referenced.