**I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jippo@campus.ie and I will add you to the mailing list.**

## This Week

On Wednesday we had our test and on Thursday we finished section 4.2 and have gotten as far as the second example in section 4.3.

In the tutorial we did p.48 Q. 2-4 and p. 59 Q. 3(a). We also spoke about the following integrals:

### Exercise from Notes

Redo Example 2 from section 4.2 using the formula we derived in section 4.3. Don’t make the same mistake I did in deriving this second formula — this needs a bit more care…

## Test Results

I won’t have them as fast as I’d like is all I can say. I’ll do my best.

## Project

Now that the test is over you may begin thinking about your project/homework. You have a choice of *six* projects — one for each full chapter. The final date for submission is 24 April 2012. You have full freedom in which one you want to do and can hand up early if you want. Please submit to the big box at the School of Mathematical Science. If I were you I would aim to get it done and dusted early as this is creeping into your study time and is very close to the summer examinations.

Note that you are free to collaborate with each other and use references but this **must be indicated on your hand-up in a declaration**. Evidence of copying or plagiarism will result in *divided marks* or *no marks *respectively. You will not receive diminished marks for declared collaboration or referencing although I demand *originality of presentation*. If you have a problem interpreting any question feel free to approach me, comment on the webpage or email.

Ensure to put your name, student number, module code (MS 2002), my name, and your declaration on your homework.

## 4 comments

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April 18, 2012 at 11:47 am

EMHi-

Having trouble with the project! doing project 4 on areas and volumes. In Q2 im struggling with integrating the u(x). your hint says to substitute x=r sinQ and then use indentities? do you substitute the x= r sin Q so the equation

u(x) is now the sqroot of r sq – rsinQ sq??

April 18, 2012 at 12:12 pm

J.P. McCarthyEM,

If we do as you suggest and let , we have

.

Now note that

using the identity .

Now what about ?

Regards,

J.P.

April 18, 2012 at 12:15 pm

Student 10I am trying to finish the MS2002 project. I choose the second one and i am stuck on question 3 part e. I was wondering could you help me with the contection between part e and a. i dont know how to connect the triangle to the intergal equation. If you assist it would be a great help as question four relys on my understanding of question 3.

April 18, 2012 at 12:21 pm

Student 10We have, in part (d), the integral in terms of . However the original integral was with respect to so we must answer in terms of . If you have correctly drawn the triangle in question 3(a) you should have in a right-angled triangle with opposite and the hypotenuse equal to . Now use Pythagoras to find the side adjacent to …

When we have done this we can find . These should be in terms of . Now replace the cosines in Q. 3(d) with this expression to get the answer given in part (e).

Regards,

J.P.