integrals...area under the curve?

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integrals...area under the curve?

Mathematics
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Gowlet
yeah, what about em?
how do we do them...without any rule?

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well if you wanna live by no rule, then it doesnt matter HOW you do them ;) I gotta ask, what do you mean?
we have a curve with a grid...we need to count the squares and find the area under the curve
is there any more accurate way to do this than to simply count the squares?
then you just gotta do your best guess... the area of a "trapazoid" is: (base)([height rightside + height leftside] /2) right?
oh ok thanks i have another question
how would i find the average value of f(x) over an interval?
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the average of any 2 numbers is add them together and divide by 2 5+8 = 13 13/2 = 6.5 is the average between them
how big is the interval?
the average f(x) is the number of each partition added together; then divide by the number of partitions used...
the more subdivision of your interval, the more accurate your average f(x) will be
f(x)=sqrt(25-x^2)
what the integral does is divides the interval into an infinite number of peices then adds them all up to get an exact value ;)
the interval is 1<=x<=5
do you want integration? or the slower way like trapaziodal rule?
probably integration
yeah...probably :)
so we have to turn this function into a higher order...... if you dont know the techniques than it aint gonna make alot of sense to you but here they are: sqrt(25 - x^2) is a disguised "cos". x = 5 sin(t) so that x^2 = 25sin^2(t) sqrt(25 - 25sin^2(t)) sqrt(25(1-sin^2(t))) = 5cos and then we can integrate:
[S] 5cos(t) dt -> 5sin(t) +C but since we got and interval we can forgo the +C part.
and thats the place I get lost at in doing this lol What I need is someone smarter than me to come along and tell me what or why I cant do it like this ;)
thats my mistake....sqrt(1-sin^2) = cos^2...not cos; got it:)
....nah, I was right to begin with....if you got a show you can watch, now would be the time to do it ;)
This is what I get for the area 978.338522 and Im like 67% sure im right lol
yep, 98% sure 978.338522

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