There are more questions below than what you need to hand in. You choose, which ones to hand in.

Submit for marking a total of 15 solutions to questions (not more). Of the questions that you hand in, 13 need to be analytically solved (handwritten or typeset) and 2 need to be Mathematica based questions.

Each analytic question weights 6pts/100; each Mathematica based question weighs 11pts/100.

In your hand-in, please try and order the questions in ascending order. Also, for each question please try to note both the number of the question as appearing below as well as the example number. It is best if you place the Mathematica based questions last, making sure to submit both Mathematica code and output.

1. Reproduce example 192.
2. Reproduce example 193.
3. Reproduce example 194.
4. Reproduce example 198.
5. Integrate x^2 * exp(-x) for x in the range [0,infinity).
6. Reproduce example 199.
7. Reproduce example 200.
8. There are a well known formulas for the volume of a sphere, a cone, a prism and many other simple three dimensional shapes. Describe how to determine these formulas via the use of integrals (perhaps double integrals). Then evaluate the integrals to obtain the respective formula (you may use Mathematica as an aid for this part if needed). Each well known three dimensional shape (of your choice) counts as a question.
9. Reproduce example 201.
10. Reproduce example 202.
11. Reproduce example 204.
12. The double (improper) integral over the whole plane of e^{-(x^2+y^2)} is fundamentally important in statistics. Evaluate this integral using a transformation to polar coordinates.
13. Use the a norm to describe the set of points in the plane that make up a circle of radius r.
14. Revisit the Cauchy-Schwartz inequality for vectors in Euclidean space: |< u,v >| < = ||u|| ||v||. Prove it.
15. Reproduce example 208.
16. Mathematica exercise 98 lists 10 integrals. Evaluate each of these integrals by hand (each integral counts as a question).