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which problem exactly?
all of them , i just want to know which formula's i need to use so that i can solve them all .
first of all find the critical points i.e. dy/dx=0 then proceed further when the slope is +ve or -ve between those intervals
r u from india?
ok...any other questions?
why would you need critical points for this problem...? it's one of those rectangle approximating things that everyone hates lol
everyone hates ? :)
I thought critical points could help in drawing the graph...could be wrong..
who needs to approximate when you can just integrate :P i always just do it and forget it
id say integrate really :)
why learn to walk if you are running marathons?
wait...so what am i supposed to do :O
you are supposed to learn that doing it the long and tedious way is proof that the shortway is better....
im not running marathons im barely even walking lol
when you have a function that is difficult to integrate, you can approximate the area under its curve thru numerical stuff like the trapaziod rule or simpsons rule and other time consuming methodss
but these? really? lol
what do you mean but these? i dont understand anything yo u just said /:
[S] -x^2 +4 dx [0,2] F(x) = -x^3/3 + 4x ....at 0 its useless so solve for 2 -8/3 + 12 = -8 +36//3 = 28/3
and I mess up doing simple multiplication lol....4(2) = 8 ;)
-8/3 +8 = -8 +24//3 = 16/3....maybe :)
integrating isnt the answer she wants though
its the answer, just not the "way" :)
you wont get teh same answer by approximating
you will if you take the reaimann sums and sll that fun stuff...right? if I recall correclt?
with inscribed and ourscribed rectangles you get the average and yadayada...
yeah but reimann sum is taking an infinite number of rectangles, this is just like a few boxes
then lets do boxes ;) we have to do it inscribed and outscribed.. but Im pretty sure you end up with the average being the limit of the 2..
mean value theorum or some such....
y'all are confusing mee /:
y = -x^2 + 4 find your f(x) values for your little rectangles.... do left right sides
y = -.5^2 + 4 y = -1^2 + 4 y = -1.5^2 + 4 y = -2^2 + 4
the area of each "rectangle" is gonna be .5 * its y value
then add the areas up
I can draw a picture if you like :)
each place a corner touches the curve; we get a value for y right?
\: im still confused . i guess i got lost along y'alls "discussion" ..
do you see the rectangles I drew? they have a width and a height right?
the right edge of each rectangle hits the curve...and stops because we drew if INside the curve.... inscribed
we are told that we do this every .5 units..... so the width of each rectangle is .5 makes sense?
good, then all we need to figure out the area of any given rectangle is ...we already now its width (.5) is going to be its height...right?
so at the first interval where x = .5; we go up until we hit the curve of y = -x+4 sine the value of "y" is our height we need to use the equation to figure out the height at x = .5 y = -.5^2 + 4 y = -2.5 +4 y = 1.5 is this right?
and of course I forgot how to square decimals...... -(.5*.5) = -.25 4-.25 = 3.75 thats better
at our next step, .5 + .5 = 1. we stick x = 1 into our equation to get the height for the second rectangle; width = .5 and height =-x^2 +4. h = -(1^2) + 4 h = -1 + 4 h = 3 Area2 = .5 * 3 = 1.5
at our next step, .5 + .5 +.5 = 1.5 we stick x = 1.5 into our equation to get the height for the third rectangle; width = .5 and height =-x^2 +4. h = -(1.5^2) + 4 h = -2.25 + 4 h = 1.75 Area3 = .5 *1.75 = .875
at our next step, .5 +.5 +.5+.5 = 2 we stick x = 2 into our equation to get the height for the third rectangle; width = .5 and height =-x^2 +4. h = -(2^2) + 4 h = -4 + 4 h = 0 Area4 = .5 *0 = 0 Do we really need to include this one? lets assume no :)
Now we add up all the areas of our rectangles: A1 + A2 + A3 + A4 = answer 1.875 + 1.5 + .875 + 0 = answer 1.875 + 1.5 + .875 + 0 = 4.25 this is the smallest value for the area under the curve that is reasonably close to the actual area under the curve. Any of this make sense?
if any of this doesnt make sense.....let me know.
im sorryy if i'm making you impatient but my mind is VERY blank right now /:
im not impatient dear :) just wanting to help you see what you really already know ;)
tell me what you are having trouble with...and I can explain it better for you.