Question

Hello , Since finals are coming , you guys are going to see me a lot here : D anyways I've gone through some questions and I wanted to check if the answers were right , I'll post them IN a second...

Answer 1

1:

\[\int\limits_{0}^{1} \frac{ 4x +2 }{ (x^2+x+1)^3 }\]

My solution:

I would do this :

take a common number 2 so I'll get:

\[\frac{ 2x+1 }{ (x^2+x+1)^3 }\] dx

so now the derivative of the denominator equals the numerator , but I don't think it would work since we have a cube , what should I do ?


---

2)


\[\int\limits_{1}^{infinite} \frac{ 2 }{ 1+4x^2 }\] dx

My solution:

I would take 1/4 as a common number and get rid of the 2 then I'l get:

\[\frac{ 1 }{ 1/4+x^2 }\]

which is \[1/2 \tan^{-1}(2x)\]

---

3)

the series from k=0 to infinity for :

\[\frac{ 2k^3 }{ 3k^3 -2k +1 } - \frac{ 3 }{ 2^k }\]

My solution:

since the limit for the first series equals 1 then it's divergent and the other one is also divergent since the first one does.

---

and this one I didn't really understand what he wants , could you guys help ?

question:

Evaluate the area enclosed by the curve corresponding to the following parametric equations:

x(t) = sin(3t)
y(t)=2cos(3t)-1

0<=t<= pi/2

Answer 2

take (x^2+x+1)=u
so
( 2x+1)dx=du
now just substitute

Answer 3

So it's -4/(x^2 +x +1)^2

Answer 4

no \[2\int\limits_{1}^{3}\frac{ du }{ u ^{3}}\]

Answer 5

do u get it?

Answer 6

Ok , if it was du/u^3 we can't use lnu^3 since it is not equal to du " the derivative "

Answer 7

no

Answer 8

(u^-3)du

Answer 9

yeah we cant use that

Answer 10

I'll solve it after finishing the series chapter , hopefully I would get it , could you guys check the other ones ? specially the last one since I didn't get it at all.

Answer 11

after integration we will get
(u^-3+1)/(-3+1)

Answer 12

thanks guys , as I said I'm more worried about the last one since that chapter we finished it only in 1 week so I didn't get it at all :D

check the other ones please.

Answer 13

the graph will look like that
http://www.wolframalpha.com/input/?i=intersection+of+y%3Dsin3t+and+y%3D2cos%283t%29-1+graph

Answer 14

I prefer not to graph :D what's the algebraic way to do this ? graphing could get hard sometimes so it's not part of the exam.

Answer 15

Where are you guys :(

Answer 16

Usually have to create a post for each question since it might be assumed you only asked 1 question and that it was answered, close the question and ask a new question and it will most likely get looked at

Answer 17

Oh , thanks buddy , I think i'll close this one then :D