3U Maths Question Thread

[RuiAce]

[jamonwindeyer]

Thanks Jamon

Anyways I am confused with the following inverse trig integration questions

For the first Integral I attached below, why do we remove 1/2 out to the front?

Ignore the second because I believe that this is a similar principle to the first

For the third why do we use polynomial long division?

Also could someone please help me with the second attached file and explain the theory behind this because I'm not too sure what the underlying theory behind this is (I mean I've seen the working to it but I don't understand what's going on)

Thanks

Hey! And the first one turns into one inverse trig integral and one logarithm integral with that factorisation applied. Breaking down the expression:



So that term on the left is an inverse trig integral, the one on the right is a log. I'll leave a formal answer to you, but the final answer you get should be (assuming I is the initial integral):



You could adjust how that logarithm is expressed if you wish 

Edit: Wait, I made a stupid assumption actually, that first one isn't an inverse trig integral. I fell into a pattern, apologies. Rui is right, that first one cannot be solved easily by 3U methods 

[RuiAce]

Thanks Jamon

Anyways I am confused with the following inverse trig integration questions

For the first Integral I attached below, why do we remove 1/2 out to the front?

Ignore the second because I believe that this is a similar principle to the first

For the third why do we use polynomial long division?

Also could someone please help me with the second attached file and explain the theory behind this because I'm not too sure what the underlying theory behind this is (I mean I've seen the working to it but I don't understand what's going on)

Thanks

Wait woah woah woah woah woah.

That Q1 is not a 3U question.

[jamonwindeyer]

Wait woah woah woah woah woah.

That Q1 is not a 3U question.

Too true, fell into my pattern there aha woops you'll need partial fractions conic!! That's a 4U concept 

[conic curve]

Too true, fell into my pattern there aha woops you'll need partial fractions conic!! That's a 4U concept 

This was the working to it (attached below)

[RuiAce]

This was the working to it (attached below)

Explain how your minus became a plus

[conic curve]

Explain how your minus became a plus

Whoops sorry I made an error. The original was supposed to be Integral of (2+x) over (1+x^2) ahaha sorry 

The thing is I don't get the underlying theory behind this and why we move 1/2 in front of the integral 

[RuiAce]

That's what did it then.


Woop. Jamon beat me

[conic curve]

Thanks for the help 

Anyways the very moment I made a minor mistake, I scared the living daylights out of everyone ahaha

Sorry about that guys 

[massive]

Hey guys, i just have a quick question; many application to the physical world questions have a question where they basically say "describe the movement of the particle". I was just wondering how you interpret the displacement, velocity and acceleration to describe its motion? Like if one is positive and another is negative, or if all are negative or all are positive, and combinations like that. Also what is a limiting position
Thanks heaps!! 

[RuiAce]

Hey guys, i just have a quick question; many application to the physical world questions have a question where they basically say "describe the movement of the particle". I was just wondering how you interpret the displacement, velocity and acceleration to describe its motion? Like if one is positive and another is negative, or if all are negative or all are positive, and combinations like that. Also what is a limiting position
Thanks heaps!!

You need to understand what motion actually is in the context of our course.

When we talk about motion, we are talking about motion on a straight line. We define a point called the origin (at x=0) and the particle either moves to the left of it, or to the right of it. We define positive displacement as the particle being to the right of the origin, and negative displacement being to the left of the origin. The value of x tells us basically how much to the right/left it is.

What do you mean by combinations? Just analyse each particle separately if you have two or more of them. Don't juggle multiple things at once without reason.

You should well know that velocity describes the rate of change in the displacement. But because we defined positive as right and negative as left, if a velocity is positive it is moving towards the right. Conversely, if it is negative, the particle moves towards the left. v=0 is described as "at rest" because the particle doesn't move.

You should also well know that acceleration describes the rate of change in the velocity. This tells us whether the particle is speeding up or not. If a=0 then the particle is moving at constant velocity (or constantly at rest, if a=0 and v=0 simultaneously). If a is positive, the particle is trying to accelerate to the right, whereas if a is 0, the particle is trying to accelerate to the left.

E.g. x=0, v=2, a=-5: Particle at the origin, moving to the right at 2ms^-1 however accelerating back towards the left at 5ms^-2

When they ask about a limiting position, however, they are talking about what happens to the particle as time goes to infinity. If you got something like x=e^-t+1, then clearly as t approaches infinity, e^-t approaches 0. So the limiting position is x=1
You should have seen something similar with limiting velocity in the context of the 4U course

[massive]

Hey guys, how do you do part ii and iii.

[RuiAce]

Hey guys, how do you do part ii and iii.

[conic curve]

Am I wrong or are the answers wrong?

[massive]

(Image removed from quote.)(Image removed from quote.)

Hey thanks so much for the reply. I was just wondering, is the time of flight 20 seconds for both particles. because the answers say that for particle A its 20s but for particle B its 10s. You think the answers are wrong?