Mathematics Question Thread

[RuiAce]

Is it mostly used for non-elementary integrals who don't have a primitive?

Well yes, because if it has a primitive then provided we can assume the Fundamental Theorem of Calculus we have no reason to not use it.

It's important regardless though. Just not taught in high school in a useful manner.

There is a whole variety of things that can be known as "numeric methods". Another is the estimation of roots in MX1.

It can be, but that integral Rui provided has a primitive (right Rui?), it would just be flat disgusting to actually do that integral but I mean yeah, pretty much! In the HSC it is mostly associated to physical scenarios where using a series of measurements to make an approximation is easier than fitting a function to the phenomena

It does but it can't be expressed in terms of the elementary functions. According to Wolfram, it's what's called the Fresnel integral. Much like how this one is handled with the error function

[jamonwindeyer]

It does but it can't be expressed in terms of the elementary functions. According to Wolfram, it's what's called the Fresnel integral. Much like how this one is handled with the error function

I miss when elementary functions were just functions, and non-elementary functions were just magic 

[RuiAce]

I miss when elementary functions were just functions, and non-elementary functions were just magic 

Ahahahahahaha well you can express them as a Taylor series if you want?

[Rathin]

I have found some good non elementary integrals. What do you think is a easier method? Trapezoidal rule or Simpson's rule?   

[RuiAce]

I have found some good non elementary integrals. What do you think is a easier method? Trapezoidal rule or Simpson's rule?

Um, easier is relative to each person. Which formula do you find easier?

Also, these are indefinite integrals. Numeric methods are for definite integrals.

[Rathin]

Um, easier is relative to each person. Which formula do you find easier?

Also, these are indefinite integrals. Numeric methods are for definite integrals.

Not too sure which one I find easy tbh
Oh and yeah..ill just add my own boundaries haha

[RuiAce]

Not too sure which one I find easy tbh
Oh and yeah..ill just add my own boundaries haha

Well in that case the answer to your question is probably that they're equally 'easy'

[Rathin]

Help with q4 and 5
http://imgur.com/14AQTWj

[RuiAce]

Help with q4 and 5
http://imgur.com/14AQTWj

[Rathin]

For q4 I got the answer which you got for q5..why did you split the two areas in q4 and not q5?

[RuiAce]

For q4 I got the answer which you got for q5..why did you split the two areas in q4 and not q5?

Because in Q5 the area was just sandwiched between two areas. BOTH of these areas ranged from 0 to 3

In Q4, one of the curves was ONLY above 0 to 1, whereas the other curve was ONLY above 1 to 3.
The key point is that the integral measures the area under the curve, but only of the SPECIFIED x-coordinates

I think maths in focus addresses this little section pretty well with examples

[Rathin]

Because in Q5 the area was just sandwiched between two areas. BOTH of these areas ranged from 0 to 3

In Q4, one of the curves was ONLY above 0 to 1, whereas the other curve was ONLY above 1 to 3.
The key point is that the integral measures the area under the curve, but only of the SPECIFIED x-coordinates

I think maths in focus addresses this little section pretty well with examples

Oh I see..the shaded area is for q5.

[Rathin]

Actually I am really confused..I dont even know what area I am finding for q4..

[jamonwindeyer]

Question 4 is a compound region:



It's the little pocket underneath both curves, the weird triangular thing (Rui provided that integral earlier, its correct)

[RuiAce]

Actually I am really confused..I dont even know what area I am finding for q4..

I double checked. It's as I said - that weird triangle-like thing at the very bottom.

Look carefully. That tiny region is bounded by all four things at once: f(x), g(x), x-axis, x=3

Question 4 is a compound region:



It's the little pocket underneath both curves, the weird triangular thing (Rui provided that integral earlier, its correct)

I doubted myself briefly whoops