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Hi guys, here's a question which I was trying to do using cylindrical shells (slicing involves integrating inverse trig) Q. Find the volumes of the solid of revolution when the arc of the curve y=sinx from x=0 to x=pi/2 is rotated about the y-axis. ----------- My working out: A(y) = 2pi(r)(h)...

AHHHH SHIT SHIT , i meant x=(4-2y^2)^0.5 guys can u please re do my question? i forgot the fucking 2

Hi guys quick question here: We have the graph x^2 = 4 - 2y^2 --> obviously it is an ELLIPSE but what if we take the positive square root the of the graph? i.e. x = (4-2y^2)^0.5 --> how will this graph look like? I had previously thought the graph x = (4-2y^2)^0.5 would have been the TOP...

Hi guys, quick question, I'm kinda new to inverse functions so I need a bit of help.. We have f(x) = x^2 + 2x + 2 = (x+1)^2 + 1 Find the inverse function of f(x) My working: Ok so restrict the domain to x(>)-1 Then x = (y+1)^2 + 1 x-1 = (y+1)^2 therefore y = +/- (sqrt(x-1)) - 1 So as you...

Thank you very much nightweaver! and Hermes! but just a side question about solving limits in the form of the above quote. What is the rule when doing limits involving products? I.e. for addition/subtraction you can split them, but what do you do for multiplication? Do you just find the limits...

Hi guys, need some help on 3 questions involving limits as x--> 0 for certain trig functions I can do simple questions like lim x-->0 (sin5x)/(2x) But here a few questions which I don't get: Q1) lim x-->0 sin2x/tanx Here's what I did: 2sinxcosx/(sinx/cosx) =lim x-->0 2(cosx)^2 --> How do...

Just to let you know, i'm not doing umat. A lot of ppl that have I've talked to have said section II is ridiculously hard. I don't understand why it is hard, I mean you just have to adopt an empathetic state of mind.... Just to have a look, could someone post a few Section II question, so i can...

wierd question, do you mind posting the solution

Hey guys, as part of an improper integral question, I ended up with a limit which I don't know how to solve; Here's the question: Integrate (x^2)(e^(-x)) INTEGRAL LIMITS: 0(<)x(<)+inf Now the limit I ended up with was: as t-->+infinity [-(t^2)*(e^(-t)) - 2t*e^(-t) - 2e^(-t) + 2] The...

Sorry, how would the upper bound be infinity? I mean u=tan(x), so when x=pi/2, u=undefined.... isn't it? I mean its not u=inverse tan x, so inverse tan (pi/2) = infinity...? Can someone please offer an explanation? Thanks

Ok, problem, I actually modified and simplified the problem just to get some hints into how I'd solve my question, the real question was: INTEGRATE: 1/(3cos^2 x + 4sin^2 x) 0(<)x(<)pi/2 which = INT 1/(3+sin^2 x) 0(<)x(<)pi/2 Following deterministic's advice: = INT (sec^2 x)/(3sec^2 x +...

pure genius, wouldn't have seen that in a million years, thank you very much.

Hi guys, how would you go about integrating these? Q1. 1/(1+(sinx)^2) Q2. ((sinx)^2)/(1+(sinx)^2) Q3. cosx/(1+(sinx)^2) Any hints or tips that do NOT involve the t-formula would be extremely helpful :)

Need help with another question: INTEGRATE [(cosx)/(4+5cosx)] I tried using t-formula, and ended up with having to integrate (1-t^2)/[(9-t^2)(1+t^2)] --> and I really don't want to use partial fractions... Anyone see a faster method to integrate this? As always, help is immensely appreciated

Q1 is a joke -- most of the time, but often you might get some harder integration in Q4/5...

yep I did what you said and got the same answer, (but it was longer than Drongo's method) Fuuarkk... is there any way to know the fastest integration method? Or is it just practice...?

can someone confirm whether this is true? can t-formula only be used on integrals in the form of dx/(a+bcosx + csinx)? EDIT: for the question, integrate (1+cosx)/(1+sinx), the answer was: -2/[1+tan(x/2)] + ln(1+sinx) + C How did Coroneos achieve this answer?

I think he deleted his comment :S

yeah what the other guy said, thankyou for the fast method! but do you see any way with using the t-formula?

Lol jeez Drongos, I already got the answer.. you didn't have to waste time with that massive solution lol... and i know this is the billionth time I've asked for help, but could someone please outline how to do this: Q. INT (1+cosx)/(1+sinx) dx I used t=tan(x/2) and after simplification...