hey find this limit for me thanks

M

mox

Veteran XV
k this is from a quiz.

i need to find the area under the curve y=4-x^2 over the interval [-1,1] using the limit technique.
I got 8, but now i'm thinking that's wrong.

Basically here is the work i got

a = h x w
h = f(w)
w = b - a / n <--- (1 - (-1)) / n where n is the number of sections and approaches infinity

so w = 2/n which means that

a = [(sigma)4 - (2/n)^2)](2/n)

i got that to

[(sigma)4n - (sigma)(2/n)^2] * (2/n) (sum total of heights times width)

here is where i'm now second-guessing what i did. I said that when N goes to infinity "(sigma)(2/n)^2" becomes negligible, leaving you with
a = (sigma)4n * 2/n
a = (4)(2)
a = 8

I'm thinking that maybe i can't make that jump.
Keep in mind this might all be wrong because for some reason i seem to suck ass at calc.
hope this makes sense.
 
you guys sure about that?
this calculator program i wrote tends to suggest that it would be more like 7.33333 :/
 
Actually, I didn't do the integral. You can just do a definite integral though for the answer.
 
limit.jpg

that's basically my work.
the part with the arrow pointing to it is i think wrong. in retrospect i don't think i can just say that it approaches 0, i think i have to actually translate (sigma)(2i/n)² into its equivalent :/
 
Finding area under a curve with limits is gay...well finding area under a curve is gay anyways. :|



moxnewb.jpg
 
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