y=2sinx help (1 Viewer)

[crammy90]

Sketch y=2sinx for -pi<=x<=pi
without integrating, evaluate the area bounded by the curve y=2sinx for -pi<=x<=pi and the x axis
so the answers did from 0 to pi/2 and multiplied by 4.
how come we dont do the 2xintegral(0-pi)?
because i dont understand why we can do this without an integral if we are finding area. i thought integral was finding area :S

 

[QuLiT]

well does it say evaulaute the integral or find the area? if it says evaluate teh integral then it would just be 0 since its an odd function

 

[tommykins]

回复: Re: y=2sinx help

Sketch y=2sinx for -pi<=x<=pi
without integrating, evaluate the area bounded by the curve y=2sinx for -pi<=x<=pi and the x axis
so the answers did from 0 to pi/2 and multiplied by 4.
how come we dont do the 2xintegral(0-pi)?
because i dont understand why we can do this without an integral if we are finding area. i thought integral was finding area :S

simpsons rule perhaps?

weird they don't want you to integrate :S

 

[crammy90]

this was part ii. part i was to evalute the integral y=2sinx between -pi<=x<=pi (answer was 0) and part ii was to evalute the area between the curve and the x axis without integrating.
so jw why 4x(from 0-pi/2) gave us the answer aka how we found the area without integrating at all.
and why couldnt we do 2X(from 0-pi)
the answer to this ii part,
they do
A = 4 x 2sin(pi/2) = 8
and how could u tell it was odd from looking at it?
and what does an equation being odd or even tell you?

 

[QuLiT]

well i know as a fact that y= 2sinx is odd but to show it, you use the graph and show it has point symmetry about the origin. and the integral of an odd function with limits a->-a is 0

 

[dolbinau]

Test odd (f(-x)) = -f(x)

Odd/Even will tell you whether it's symmetrical about the (origin?) or not.

 

[QuLiT]

Test odd (f(-x)) = -f(x)

Odd/Even will tell you whether it's symmetrical about the (origin?) or not.

you cannot use f(-x) = -f(x) for sinx since you need to use the fact that it is an odd function to prove that.

and even function is symmetrical about the y-axis an odd function has POINT symmetry about the origin

 

[dolbinau]

you cannot use f(-x) = -f(x) for sinx since you need to use the fact that it is an odd function to prove that.

Can you explain this :S? I thought we can use that for everything

 

[QuLiT]

well, i don't know there could be a way to show that, but it's generally easier to use the graph and show it has point symmetry.

 

[Azreil]

Can you explain this :S? I thought we can use that for everything

I thought you could.

eg
f(x) = sin(pi/6) = 0.5
f(-x) = sin(-pi/6) = -0.5
ie f(-x) = -f(x)

 

[dolbinau]

well, i don't know there could be a way to show that, but it's generally easier to use the graph and show it has point symmetry.

Oh right, for actual proofs I guess but if we wanted to "tell it was odd from looking at it" I thought subbing in a value for X would be sufficient.

 

[crammy90]

so you cant tell its an odd function from the equation and just be like hey its odd itll cancel out to make 0?
or do we draw the graph, see it has a POINT of axis of symetry around the x axis and is therefore odd?

even function is symmetrical about the y-axis an odd function has POINT symmetry about the origin

so as the side to the left of the curve is beneath and not above then we declare the origin to be a point of symetry rather than an axis of symetry?
and if the curve were say x^2 it would be symetrical around the y axis and thus an even function?
i dont see when we would ever need to use this odd or even function stuff when we can just draw the graphs? what sort of questions would require us to know about odd or even functions?

 

[adnan91]

answer is zero..odd function proven by the graph and F(-x)=-F(x)

 

[QuLiT]

ok, generally, when your given a question show that the integral between -1->1 of f(x) dx is = 0 you would use f(-x) = -f(x) to show that its an odd function and then you can say that the integral of an odd function between limits -a -> a is equal to 0.

but, in the case of sinx it's not as simple as subbing in -x because to show that sin-x = -sinx you need to use the graph (pretty sure??)

 

[tommykins]

回复: Re: y=2sinx help

Sketch y=2sinx for -pi<=x<=pi
without integrating, evaluate the area bounded by the curve y=2sinx for -pi<=x<=pi and the x axis
so the answers did from 0 to pi/2 and multiplied by 4.
how come we dont do the 2xintegral(0-pi)?
because i dont understand why we can do this without an integral if we are finding area. i thought integral was finding area :S

I believe the question is asking for the AREA, not a simple evaluation.

If it was just evaluate -pi->pi 2sin dx then it'd be 0 as sinx is odd function.

 

[jolzy~~]

the way i think of it.. integration gives signed area under the curve....

so if they want an intergral, you just calc an integral

but if they want an area, you use integration along the way to find some signed areas........ then you need to work out which signs to keep and which ones to get rid of

hope that helps lol

 

[crammy90]

yeh ok thanks heaps so i understand now
does any1 have an easy way to remember the rules of
f(x) = f(-x) and f(-x) = -f(x) ???

 

[dolbinau]

And for even f(-x)=f(x)

The way to remember it, Is to understand it IMO

If you apply it to something like f(x)=x^3

Obviously because the power of x is odd a negative value will be the same as -f(x).


I don't know if it's helpful . You should have learnt it in year 11 I think?