[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

[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

[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.

[mGGPrometheus]

Oh it's just a useful trick to deal with integrals of sec^n(x)dx and cosec^n(x) where n is odd. With cosec^n(x) you would multiply the top and bottom by sin(x)

[AxS.pinealan]

Looks like a neat technic that I can use in my exams. Thx Titan!
However, I still wanna know if this is a valid answer. I got this answer after doing integration by part twice.

[mGGPrometheus]

The only sure way to know is take the derivative! It's really close but I think it's

integration by parts is a pretty sweet way to do this problem. It probably requires less work than partial fractons

Quick Comments

AxS.pinealan:

btw, how do you make those images of the answers?

[AxS.pinealan]

Oh right, I forgot the 3 when you integrate that sec^3x. Thx a lot Titan!

Quick Comments

mGGPrometheus:

http://www.codecogs.com/latex/eqneditor.php

[AxS.pinealan]

More maths is always better! Enough of calculus for the week, so can anyone help me with this parametric equation?

[Antel0pe]

Help anyone?
doing a GCSE math book on Geometry and my tuition teacher presumed I learned trigonometry ;;

I'm kinda lost T_T

[AxS.pinealan]

Originally Posted by Antelopes

Help anyone?
doing a GCSE math book on Geometry and my tuition teacher presumed I learned trigonometry ;;

For (a), use the cosine rule

Then in (b), since you know the angle POQ, you can multiple it with the radius to get the arc length. After that i guess you know how to do the perimeter.

As for (c), you need to know the area of the segment PQ. To do that, you first calculate the area of the larger part of sector POQ, which you can do so by multiplying pir^2 with the reflex angle in radians. Then, find out the area of the triangle POQ. That, you can use the sine rule.
Then you just add them up. wala.

I hope that you can understand my messy working

Quick Comments

Antel0pe:

thanks~ ^-^ with this, and some workings i did with the teacher, i think i can solve it~

[mGGNemesis]

stuff here is actually getting pretty serious

[mGGPrometheus]

Originally Posted by pinealan

More maths is always better! Enough of calculus for the week, so can anyone help me with this parametric equation?

Solve for t so that t = -1 + 1/x. Then sub that into the second equation. From there's it should just be a matter of simplifying fractions.

[Seffy]

Hey guys,

My friend sent me this picture cos she thought I was good at Mathematics.. clearly I suck LOL so I'm seeing if anyone here have any idea as to what these are, as my friend or myself have no idea what these formulae are. Thanks in advance!

Quick Comments

AxS.pinealan:

lol what are these things, got no idea what they are

[mGGPrometheus]

Top left is Fermat's Last Theorem, which is a famous problem in mathematics that was recently solved by Andrew Wiles.

Top right some kind of Fourier Series in quantum mechanics. In QM you can completely describe objects using different kinds of 'basis states', such a position, momentum, energy, spin etc. In some cases knowledge of one set of states allows you to know another set of states, thanks to the uncertainty principle. I'm not quite sure what it's saying but I think the general gist that one side of the equation is one state (e.g position), the other is another state (e.g momentum), and the equation lets you transform between the two.

Bottom left is an (Inverse) Fourier Transform. If you have a signal whose amplitude varies with time, you can analyze what frequencies it's made up of using a Fourier transform. For example, say you have a piano note being played. The time-signal will be some kind of oscillating wave. Apply a Fourier transform and you can see the different sound frequencies it's made up of. One of the frequencies you see will be the actual note, however you may also see higher frequencies contributing to the timbre of the instrument.

Bottom right is some kind of inner product in quantum mechanics (similar to a dot product except with functions instead of vectors).

Dunno what the middle is

Quick Comments

	Seffy:	Thanks Titan! Helped my friend a lot. :)
	AxS.pinealan:	0.0 you are so good at maths, and you even know about QM stuff

[eCKo`Tazerenix]

Let ε < 0.