[mGGPrometheus]

Originally Posted by pinealan

lnlsecx+tanxl + C
thats an identity in my textbook which I am supposed to memorize =P

Yep, although I never thought that was the obvious solution. An alternative solution is to multiply the top and bottom by cos(x) and use the substitution u = sin(x).

[Mukade]

ln (tan x + sec x) +C, lol, ez

[AxS.pinealan]

Well, my solution is to multiply the top and botton by (secx+tanx)

[FlashVeno]

3+100÷5(2)

is brackets the same as times? if it is then its 43
but if you follow bodmas brackets are first, so its 13
wolfram alpha says 43..what do you guys think?

[|Erasmus|]

you evaluate the (2) first, not the 5 x 2 cause that's not what's in brackets.

wolfram alpha is 100% correct.

Quick Comments

mGGAequitas:

wolframalpha is always correct :)

[TheGentleman]

I thought I'd do this graphically for you cause it looks better ^^



I find it's best to look at the equation written in fractions like so:



Because it can also be written like so:



At this point in time it's up to you how you solve the equation. You can either multiply the Numerator of each fraction and Denominator of each fraction by each other to get this:



OR you can resolve each fraction first and then multiply the numbers left behind by each other like so:



Either way the answer is the same. The important thing to note is that 100 is the numerator and 5 is the denominator of fraction one while 2 is a fraction on its own. 5 * 2 is multiplying the denominator of one fraction by the numerator of the other and is the reason why 13 is not the correct answer.

i.e. is the problem.

I hoped this helps

+ [old content... now irrelevance] +

3+100÷5(2)

expands to look like this:

3 + ((100 / 5) * 2)
= 3 + (20 * 2)
= 43

OR

3 + ((100 * 2) / 5)
= 3 + (200 / 5)
= 43

in short yes... brackets indicate multiplication unless otherwise specified.

Edit:

Originally Posted by |Erasmus|

you evaluate the (2) first, not the 5 x 2 cause that's not what's in brackets.

Actually... the 2 is in brackets on its own so technically the stuff within the brackets is already resolved and it just indicates multiplication. Then it's simple BOMDAS... considering Multiplication and Division are considered equal it doesn't matter whether you perform 100 / 5 first or 100 * 2 first... just as long as you don't do 5 * 2 because 5 is a denominator not a numerator.

P.S. I read eras' message wrong confusing me ^^ still all information is good information.

[|Erasmus|]

yeah... that's what i said... it's just (2) inside the brackets, so only the 2 is evaluated by bomdas. so you don't do 5x2. which gives the alternative (wrong) answer 13

Quick Comments

TheGentleman:

ah right... nvm... I just tripped over the terminology that was used <.< My bad.

[FlashVeno]

thanks now i know xD
i thought it was 13 before lol

[syfPhoenix]

So much of the stuff in this thread has gone over my head... :S im screwed when i get back to school T_T

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eCKo`Tazerenix:

Most of it is uni level anyway

[AxS.pinealan]

Was working on some public exam past papers when I stumbled upon this:
Intergrate

I have no idea how to do this T.T

Edit: thx for telling me that link didnt work, i'll just write it here
Int sec^5(x) dx

Quick Comments

	|Erasmus|:	link no work for me...
	mGGPrometheus:	^
	Mukade:	Not for me either. You know how much I love doing your maths problems for you :P

[mGGPrometheus]

Originally Posted by pinealan

Was working on some public exam past papers when I stumbled upon this:
Intergrate

I have no idea how to do this T.T

Edit: thx for telling me that link didnt work, i'll just write it here
Int sec^5(x) dx

As in the previous problem, you can multiply the top and bottom by the same factor:

The result follows by u-substitution.

[ToRSpartaz]

Reading some of these calc equations makes me just want to study again >< not a good sign O_o

Quick Comments

FaDeBadger:

This, loved it in High school

[AxS.pinealan]

er, I still cant work out the answer... do I have to use integration by part?
What I now have is
Not sure if it is correct. May I ask for a bit more help?

[mGGPrometheus]

Originally Posted by pinealan

er, I still cant work out the answer... do I have to use integration by part?
What I now have is
Not sure if it is correct. May I ask for a bit more help?

After letting u = sin(x), du = cos(x)dx, the integral becomes . Then you just need to use partial fractions.



Since this must be true for all u, we can try different values of u. Letting u = -1, we see that D = 1/8. Letting u = 1, A = 1/8. Letting u = 0, A+B+C+D+E+F = 1, so B+C+E+F = 3/4, so B = 3/4 - C - E - F. Then you expand the RHS so you get a cubic in 'u' and equate the terms on both sides to solve for the other constants. In the end you get



And ^ can be integrated pretty easily. I didn't want to type the working out because it's quite a messy problem

[Mukade]

Originally Posted by mGGTitan

After letting u = sin(x), du = cos(x)dx, the integral becomes . Then you just need to use partial fractions.



Since this must be true for all u, we can try different values of u. Letting u = -1, we see that D = 1/8. Letting u = 1, A = 1/8. Letting u = 0, A+B+C+D+E+F = 1, so B+C+E+F = 3/4, so B = 3/4 - C - E - F. Then you expand the RHS so you get a cubic in 'u' and equate the terms on both sides to solve for the other constants. In the end you get



And ^ can be integrated pretty easily. I didn't want to type the working out because it's quite a messy problem

Good working o.0 I wish I'd thought of that.

[Mukade]

That's a really hard problem pinealan. I think you have to use the reduction formula for sec^n (x), no idea what it is though, sorry.

[Mukade]

http://en.wikipedia.org/wiki/Integral_of_secant_cubed That should have them!

[faithHunter]

Kinda off topic but can someone explain to me what exactly is a Tesseract? The youtube videos I watched said that its a "cube inside of a cube" but when you rotate it it gets really really weird and incomprehensible IMHO.

[eCKo`Tazerenix]

Originally Posted by faithHunter

Kinda off topic but can someone explain to me what exactly is a Tesseract? The youtube videos I watched said that its a "cube inside of a cube" but when you rotate it it gets really really weird and incomprehensible IMHO.

Basically if a square is a 2D 'square' and a cube is a 3D 'square', a tesseract is a 4D 'square'. The thing to understand about dimensions is a dimension is defined as being perpendicular to all other dimensions. Now in 2D or 3D space we can easily visualize this but we can't in 4D space, because we live in 3D space. When people say a tesseract is a cube inside a cube with the verticies joined, thats not actually a tesseract, its the shadow of a tesseract viewed in 3D space, much like you can draw the shadow of a cube in 2D space. Scientists just sort of added a dimension and did some analysis and thinking to figure out what the 3D shadow would look like. Since we can't actually visualize a tesseract, scientists or mathematicians try and make visualizations for it with computers, with stupid videos and gifs of a tesseract rotating, but these dont actually mean anything because to grasp it you need to see 4D space which is impossible for 3D species.

Quick Comments

AxS.pinealan:

simply put, its not something that ANYONE can exactly explain

[AxS.pinealan]

the thing i hate about integration is that there are tons of possible representations of the answer, and I have no clue if mine is a correct one.
Another answer that I just worked out with Mukade's help:

Quick Comments

Zepph:

Is that your handwriting? It's so ridiculously neat I could eat it.