Intergrating both sides? (1 Viewer)

[shimmerz_777]

a couple of times ive seen solutions to problems in mechanics where people intergrate both sides of an equasion. i dont really get this. i think there is an example in the 2002 HSC q7 a (ii) in which i breifly saw the answer may have involved doing this but i could be wrong or just interperating it in a stupid way.
anyway does intergrating both sides exist and if so when and how do you do it

thanks

its probably just nothing more than me getting intimidated by seeing intergrals on either side of the equals sign and stuff but still rather safe than sorry

 

[Sober]

a couple of times ive seen solutions to problems in mechanics where people intergrate both sides of an equasion. i dont really get this. i think there is an example in the 2002 HSC q7 a (ii) in which i breifly saw the answer may have involved doing this but i could be wrong or just interperating it in a stupid way.
anyway does intergrating both sides exist and if so when and how do you do it

thanks

its probably just nothing more than me getting intimidated by seeing intergrals on either side of the equals sign and stuff but still rather safe than sorry

Lets say accelleration is equal to the negative of velocity then:

a = -v;

dv/dt = -v

dt = (-1/v) * dv

Then in order to get t we need to integrate both sides, it is only necessary to add a constant of C to one side:

t = -ln(v) + C

 

[housemouse]

You should be integrating both sides in resisted motion questions.

 

[Riviet]

its probably just nothing more than me getting intimidated by seeing intergrals on either side of the equals sign and stuff but still rather safe than sorry

It's spelt *integrate*

It's just like dividing both sides by a constant or differentiating both sides with respect to something.

 

[Trev]

You should be integrating both sides in resisted motion questions.

I never did in the HSC, I never even knew about it... It's a thing we have to do at uni.

 

[shimmerz_777]

Lets say accelleration is equal to the negative of velocity then:

a = -v;

dv/dt = -v

dt = (-1/v) * dv

Then in order to get t we need to integrate both sides, it is only necessary to add a constant of C to one side:

t = -ln(v) + C

i knew how to do that, it was probably just looking at the working or the way it was written which got me nervous

 

[Trebla]

Or in some cases you can avoid the constant by using limits and integrating both sides. For example you might integrate dt from 0 to t and dv from its initial value to v.

Are you allowed to do that with variables as limits in the HSC? I'm used to integrating something using constants as limits because it is finding a constant area. I know that method works out to the right answer but when using variables as limits, wouldn't this mean inserting variables into variables?