Mathematics Question Thread

[jamonwindeyer]

I keep getting this wrong for some reason..
Find the area bounded by the curves y=x^2(1-x) and y=x(1-x)^2.

A diagram of the scenario to complement Jake's answer above



You can see the two area sections Jake is talking about, and by visual inspection (symmetry ), they are equal

[katnisschung]

stuck with this indefinite integral..

i got (8x+7)^2/16 +C
but presumably they want it expanded
becos the final answer is 4x^2+7x
but somehow my 49 is not cancelling out

[Syndicate]

stuck with this indefinite integral..

i got (8x+7)^2/16 +C
but presumably they want it expanded
becos the final answer is 4x^2+7x
but somehow my 49 is not cancelling out

hmm... I think you have made a mistake.
anti-diff of 8x is \( 4x^2 \) and 7 is 7x.

So your final answer should be \( 4x^2+7x+C \)

Not sure if this rule is thought in HSC, but it is quite helpful: \( \frac{ ax^{n+1}}{n+1} \)

[katnisschung]

thanks syndicate yeah i got the first part but i expanded to get 4x^2+7x+49/16??
i obviously went wrong somewhere

[jamonwindeyer]

Not sure if this rule is thought in HSC, but it is quite helpful: \( \frac{ ax^{n+1}}{n+1} \)

Just confirming that's definitely the rule for us too cheers Syndicate!

[RuiAce]

thanks syndicate yeah i got the first part but i expanded to get 4x^2+7x+49/16??
i obviously went wrong somewhere

Remember that when integrating there is an extra +C

The constant can be anything. If you let C = 49/16 + c, then you get 4x^2 + 7x + c

Which is the same thing that Syndicate said.

(That being said, your final answer should've been 4x^2 + 7x + 49/16 + C for it to work. If you drop out the +C without a good reason, something is indeed wrong.)
(The +C is important. For example, if you integrate 2x, then x^2+C is an answer, but so is x^2+4+C)

[jamonwindeyer]

thanks syndicate yeah i got the first part but i expanded to get 4x^2+7x+49/16??
i obviously went wrong somewhere

Edit: More detailed version of what Rui said

Ahh, I've figured out your mistake!

So you are using this rule:



So this rule is actually a little bit overkill for this question - You are way better off just tackling each term one at a time as Syndicate outlined above. If you do want to use this rule, it works, you get this:



But Syndicate (and the answers) get:



They are actually the same thing! It's just that the constant (\(C_1\)) in your answer is a different value to the constant (\(C_2\)) in Syndicate's. Both are arbitrary constants, so this is irrelevant.

You have definitely not taken the most efficient approach. Your working was likely about 4-5 lines - Doing it term at a time only takes one. But, you are correct nonetheless

[RuiAce]

Well I mean, the rule \(\int (ax+b)^n dx = \frac{(ax+b)^{n+1}}{a(n+1)} \) can be used in one line as well. But yeah it's overkill; term by term integration should be favoured where no effort is needed (e.g. some binomial theorem expansion).

[jamonwindeyer]

Well I mean, the rule \(\int (ax+b)^n dx = \frac{(ax+b)^{n+1}}{a(n+1)} \) can be used in one line as well. But yeah it's overkill; term by term integration should be favoured where no effort is needed (e.g. some binomial theorem expansion).

Not all of us skip expansion/cancellation steps

[Rathin]

I am probably gonna beat my self if I make a silly mistake but I tend to do all the Primitive Transformation and indices manipulation in my head cuz It looks ugly on paper and I ceebs..even do it for square roots and stuff..

[Rathin]

stuck with this indefinite integral..

i got (8x+7)^2/16 +C
but presumably they want it expanded
becos the final answer is 4x^2+7x
but somehow my 49 is not cancelling out

They are actually the same thing.
You can Integrate them Individually or use the rule ∫(ax+b)^n = ((ax+b)^n+1)/a(n+1)
You used the latter rule.

EDIT: Jamon already mentioned this whoops

[jamonwindeyer]

I am probably gonna beat my self if I make a silly mistake but I tend to do all the Primitive Transformation and indices manipulation in my head cuz It looks ugly on paper and I ceebs..even do it for square roots and stuff..

I feel like everyone has a different balance that works for them, I'll skip certain things... But I'm probably more cautious than most, I've been stung too many times

[phebsh]

Hi everyone,

What's the best way to study for math if you absolutely hate it and are terrified of it? What are the best techniques? I tend to put it away and avoid it for as long as possible and if I get a question wrong, I'll give up imediately... I'm more of an english person. 

Thanks! 

[RuiAce]

Hi everyone,

What's the best way to study for math if you absolutely hate it and are terrified of it? What are the best techniques? I tend to put it away and avoid it for as long as possible and if I get a question wrong, I'll give up imediately... I'm more of an english person. 

Thanks! 

Before I reply, I must apologise for some unintended negativity that will inevitably flow out of this post.

Given that you hate it, is there a reason you chose to keep the subject?

Regardless of what subject it is, if you hate it you're not gonna try hard enough. You can push and attempt to focus, but it may not pay off.

Fact is, maths is all about practice. And getting questions wrong should not be surprising; if everyone in the state could do every maths question then we'd be questioning if our subjects were way too easy and need significant revamping. Most students push through it by eventually learning that they just have to accept that they must:
- Do some questions open book
- Look at answers if they're GENUINELY stuck
- Keep drilling in the past papers (note: emphasis on past papers over textbooks)

But if you hate it, you probably won't be able to push yourself to do all of that.

[phebsh]

Before I reply, I must apologise for some unintended negativity that will inevitably flow out of this post.

Given that you hate it, is there a reason you chose to keep the subject?

Regardless of what subject it is, if you hate it you're not gonna try hard enough. You can push and attempt to focus, but it may not pay off.

Fact is, maths is all about practice. And getting questions wrong should not be surprising; if everyone in the state could do every maths question then we'd be questioning if our subjects were way too easy and need significant revamping. Most students push through it by eventually learning that they just have to accept that they must:
- Do some questions open book
- Look at answers if they're GENUINELY stuck
- Keep drilling in the past papers (note: emphasis on past papers over textbooks)

But if you hate it, you probably won't be able to push yourself to do all of that.

The reason I kept it was because my school made math compulsory, which I'm obviously not happy about...

I'll definately put in the effort and do my absolute best. Thanks for your input!