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MATH-UA 132
Written Homework
Instructions
• This homework should be submitted via Gradescope by 11:59 pm on the date listed above.
You can find instructions on how to submit to Gradescope from this link or this video .
• There are two main ways you might want to write up your work.
– Write on a digital tablet and save in one PDF
– Write your answers on paper, then you can use an app such as WebScanner or OceLens
by Microsoft to take pictures of your work with your phone and convert them into a single
pdf file.
∗ Either way, you don’t have to copy the original question. However, you need to write
Homework title, for example Written HW 0, your name, and label each part of the
question clearly.
• Please use at least 3 pages to finish one written HW. Graders can’t give partial credits if you
Squeeze all the answers in one page or skip two many steps.
• You must show all work. You may receive zero or reduced points for insucient work.
Your work must be neatly organised and written. You may receive zero or reduced
points for incoherent work.
• When uploading to Gradescope, you must match each question to the page that your
answer appears on. If you do not you will be docked a significant portion of your score.
• The problems on Written Homework will be graded on correctness and completeness.
• These problems are designed to be done without a calculator. Whilst there is nothing stopping
you using a calculator when working through this homework, be aware of the fact that you are
not permitted to use calculators on quizzes nor exams so you might want to practice without
one.
• By all means you may work in groups on the homework assignments. However, each student
must turn in his or her own write-up of the solutions. Submitting group work line by
line, notation by notation as your own work is a violation of honor code.
MATH-UA.0132 - Written Homework 9
Exercise I: A sneaky integral
We wish to compute, for n = 0, 1, 2, . . . , the integral
In =
Z 1
0
(1 x2)n dx.
1. (3 pts) Compute I0 and I1.
2. (2 pts) Why can we not substitute u = 1 x2 in order to compute In?
3. (3 pts) Compute Z
x(1 x2)n1 dx.