contradiction - volume technique (1 Viewer)

[Abtari]

when doing volume problems, i came across problems where you had to suppose a point P (x,y) on the curve...the area under the curve being rotated around a certain axis etc..

should you change the supposed point to P(-x,y) if it is in the 2nd or 3rd quadrants and likewise should u write P(x,-y) if it is in the 3rd and 4th quadrants?

in two past hsc paper solutions, they have approached differently (.e. both 'methods' have been used in different contexts for similar questions. this is contradictory. which do we follow...ignore signs for variables OR take them into consideration??)

thanks heaps.

 

[FinalFantasy]

when doing volume problems, i came across problems where you had to suppose a point P (x,y) on the curve...the area under the curve being rotated around a certain axis etc..

should you change the supposed point to P(-x,y) if it is in the 2nd or 3rd quadrants and likewise should u write P(x,-y) if it is in the 3rd and 4th quadrants?

in two past hsc paper solutions, they have approached differently (.e. both 'methods' have been used in different contexts for similar questions. this is contradictory. which do we follow...ignore signs for variables OR take them into consideration??)

thanks heaps.

just put p(x,y)
ur x can be negative or positive depending on where P is cuz it can change
same for y..
no need to put negative signs in front of dem

 

[Abtari]

okies thanks...

so instead of say (x, y) and (-x, y) should we put (x1,y) and (x2,y) thereby ignoring where the coordinate axes are?

 

[FinalFantasy]

okies thanks...

so instead of say (x, y) and (-x, y) should we put (x1,y) and (x2,y) thereby ignoring where the coordinate axes are?

if u employ more than 1 point on ur diagram u can just make it x1, y1 or x2,y2... etc..

well atleast that's how i do it lol
u better wait and c other peoples opinion first

 

[Templar]

There really is no need to make x and y positive variables only. Both methods are valid and should yield the same answer.

Just use x and y. Additional negative signs can increase the probability of making an error.

 

[dawso]

its just like wen u evaluate an integral, whilst the constant may be "-6" for example, u simply write +c, (in which case c will be -6)

as templar said, minus signs are messy, just stick with positive for both, but just keep an eye on this throughout the question....