Bazza's 3/4 Question Thread

[pi]

i know it's not a fraction. i mean for d/e where dy/dx = f(y)
(except second order)


and what's int by parts?

If it's not a fraction, you can't reciprocate it under fraction laws.

Integration by parts (NOT on spesh course and NOT allowed in SACs/exams), so don't worry haha

[brightsky]

take the product rule, integrate both sides with respect to x, and rearrange, and you get your 'formula' for integration by parts.

and yeah, in regards to my question, point is, you can use integration by parts, but considering the inverse function and rotating that around the x-axis is much quicker and easier way to go about it.

[WhoTookMyUsername]

i know it's not a fraction. i mean for d/e where dy/dx = f(y)
(except second order)


and what's int by parts?

If it's not a fraction, you can't reciprocate it under fraction laws.

Integration by parts (NOT on spesh course and NOT allowed in SACs/exams), so don't worry haha

ah
it doesn't behave like a fraction D:

[WhoTookMyUsername]

have a go at this:

find the volume of the solid obtained when y = e^x between y = 1 and y = 4 is rotated around the y-axis.

loge(y) = x
V
 = piS(4,1)[lny]^2 dy



for diff equations
dy^2/d^2 x

does that become (when flipped)
dx^2/d^2y?

was my answer wrong D:?

[pi]

loge(y) = x
V
 = piS(4,1)[lny]^2 dy

was my answer wrong D:?

You don't have an answer yet

[WhoTookMyUsername]

oh yeah lol, but you're not required to be able to integrate ln(a) by hand are you?
(unless provided with additional information)

edit: what to include on cheat sheet
?

i have nothing for diff at the moment D:
(got a few nice WE for integ/ d/e)

[paulsterio]

Integration by parts is a technique used when you have a product of a simple function and a difficult function.

For example, we can use integration by parts in order to antidifferentiate

Remember our Product Rule:

If

Then:

So essentially:

Taking the integral of both sides, we will have

Ok, so how does this help us solve the problem of integrating

Well, what we can do is say let and

So essentially, we can see that

So it's easy enough now for us to be able to see now that



Which we can easily use a substitution and figure out using basic integration

and

Finishing off:

You won't need to be able to do that in Specialist Maths, but anyways, that's just a basic example of how integration by parts works.

[WhoTookMyUsername]

take the product rule, integrate both sides with respect to x, and rearrange, and you get your 'formula' for integration by parts.

and yeah, in regards to my question, point is, you can use integration by parts, but considering the inverse function and rotating that around the x-axis is much quicker and easier way to go about it.

OH ! WOW
NOW I GET IT
Brilliant example of what i was trying to illustrate, so you effectively integrate as is? with terminals at 1 and 4?
(e^x)

piS(1,4) e^(2x) dx ?


wait... i'm missing something here, what have i done wrong?

oh wait, aren't you still left with the same problem? having to integrate ln(x)? SOO confuzzled


and

what to include on cheat sheet
?

i have nothing for diff at the moment D:
(got a few nice WE for integ/ d/e)

[pi]

take the product rule, integrate both sides with respect to x, and rearrange, and you get your 'formula' for integration by parts.

and yeah, in regards to my question, point is, you can use integration by parts, but considering the inverse function and rotating that around the x-axis is much quicker and easier way to go about it.

OH ! WOW
NOW I GET IT
Brilliant example of what i was trying to illustrate, so you effectively integrate as is? with terminals at 1 and 4?
(e^x)

piS(1,4) e^(2x) dx ?

I don't think that's right :S

[WhoTookMyUsername]

take the product rule, integrate both sides with respect to x, and rearrange, and you get your 'formula' for integration by parts.

and yeah, in regards to my question, point is, you can use integration by parts, but considering the inverse function and rotating that around the x-axis is much quicker and easier way to go about it.

OH ! WOW
NOW I GET IT
Brilliant example of what i was trying to illustrate, so you effectively integrate as is? with terminals at 1 and 4?
(e^x)

piS(1,4) e^(2x) dx ?

I don't think that's right :S

no it's not... i thought that's where brightsky was heading but it's not D:

but considering the inverse function and rotating that around the x-axis is much quicker and easier way to go about it.

is anyone able to elaborate / clarify this?
thanks

[paulsterio]

He just means taking y = ln(x) and rotating that around x = 0 and x = ln(4)

though integrating (ln(x))^2 is a pain, but you can do it by the substitution u = ln(x)

[BubbleWrapMan]

but considering the inverse function and rotating that around the x-axis is much quicker and easier way to go about it.

is anyone able to elaborate / clarify this?
thanks

If you rotate a curve about a different axis, then in general you get a different shape and a different volume.

[pi]

He just means taking y = ln(x) and rotating that around x = 0 and x = ln(4)

though integrating (ln(x))^2 is a pain, but you can do it by the substitution u = ln(x)

I don't think that works either as the solution to the original question, does it?


edit: and even if it does, I can's see how that simplifies the question...

[WhoTookMyUsername]

If it asks for the distance between say t = 1 and t = 3

Do you have to check for turning points?
Similarly if it asks for max velocity or max distnce do you have to check if its a maximum or minimum?

I reckon technically you should do both but the textbook WS never does either

ThanksA!

[kamil9876]

If it asks for the distance between say t = 1 and t = 3

Do you have to check for turning points?
Similarly if it asks for max velocity or max distnce do you have to check if its a maximum or minimum?

I reckon technically you should do both but the textbook WS never does either

ThanksA!

I don't understand the context of your question, can you provide an example of what you mean, i.e a question etc.