Maths Methods 3/4 Help Thread 2011

[pi]

tip: expand first

[luken93]

expand and do it from there:

- 3z^2 + 5z + 2
int\{- 3z^2 + 5z + 2, dz}
= -z^3  + 5/2z^2 + 2z + c

[kefoo]

cheers
how about..
int\sqrt(x).(2+x)dx

[pi]

cheers
how about..
int\sqrt(x).(2+x)dx

Expand again:


EDIT: more hints, remember index laws, maybe an easier writing is

In case you still wanted a fully worked solution:










EDIT: thanks brightsky, lol

[brightsky]

+C :p

[epinephrine]

How do I integrate tan(x) ?

[Andiio]

How do I integrate tan(x) ?

split tan(x) into sin(x)/cos(x), should be relatively simple from then on! (sorry I don't know how to use latex )

Hope that helped!

[epinephrine]

I did the first bit but got stuck from then, so how do integrate from then?

[xZero]

remember the integral of f'(x)/f(x) = loge(f(x))

[epinephrine]

could you please explain haha I'm soo dumb!

[epinephrine]

Bump! Anyone? please?

[jane1234]

How do I integrate tan(x) ?

It's not actually required knowledge for methods. You learn how to do it in spesh.

But, if you still wanted to know then just follow what the others have said.

tan(x) = sin(x)/cos(x)

We know that d(loge(f(x)))/dx = f'(x)/f(x), therefore we know that int(f'(x)/(fx)) = loge(f(x)).

Now you know that the derivitave of cos(x) = -sin(x),

Therefore int(-sin(x)/cos(x)) = loge(cos(x))

Therefore -int(sin(x)/cos(x)) = loge(cos(x))

                      int(sin(x)/cos(x)) = -loge(cos(x)) + c

Therefore int(tan(x)) = -loge(cos(x)) + c

Like I said, I'm fairly sure this is spesh knowledge though... or else you would only be required to do this using a calculator.

[epinephrine]

Oh haha thank you!

[xZero]

How do I integrate tan(x) ?

It's not actually required knowledge for methods. You learn how to do it in spesh.

But, if you still wanted to know then just follow what the others have said.

tan(x) = sin(x)/cos(x)

We know that d(loge(f(x)))/dx = f'(x)/f(x), therefore we know that int(f'(x)/(fx)) = loge(f(x)).

Now you know that the derivitave of cos(x) = -sin(x),

Therefore int(-sin(x)/cos(x)) = loge(cos(x))

Therefore -int(sin(x)/cos(x)) = loge(cos(x))

                      int(sin(x)/cos(x)) = -loge(cos(x)) + c

Therefore int(tan(x)) = -loge(cos(x)) + c

Like I said, I'm fairly sure this is spesh knowledge though... or else you would only be required to do this using a calculator.

This is methods knowledge, if you use u-substitution method then its spesh

[happycat]

Here's 2 conditional probability Q's.
1-Pr(Nathan kicks more than 4 goals on a wet day)=0.3
Pr(Nathan kicks more than 4 goals on a dry day)=0.6
Pr(that it'll be wet on the day of next game)=0.7
What is the probability that Nathan will kick more than 4 goals in next game?

And for Q number 2- Pr( person with disease yields a positive result) 0.95
Pr(person without disease yields a positive result)= 0.02
Pr(that a randomly selected person has the disese)=0.03
What's the probability that randomly selected person yields a positive result.