anonymous
  • anonymous
integrals...area under the curve?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
Gowlet
amistre64
  • amistre64
yeah, what about em?
anonymous
  • anonymous
how do we do them...without any rule?

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amistre64
  • amistre64
well if you wanna live by no rule, then it doesnt matter HOW you do them ;) I gotta ask, what do you mean?
anonymous
  • anonymous
we have a curve with a grid...we need to count the squares and find the area under the curve
anonymous
  • anonymous
is there any more accurate way to do this than to simply count the squares?
amistre64
  • amistre64
then you just gotta do your best guess... the area of a "trapazoid" is: (base)([height rightside + height leftside] /2) right?
anonymous
  • anonymous
oh ok thanks i have another question
anonymous
  • anonymous
how would i find the average value of f(x) over an interval?
amistre64
  • amistre64
1 Attachment
amistre64
  • amistre64
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
amistre64
  • amistre64
how big is the interval?
amistre64
  • amistre64
the average f(x) is the number of each partition added together; then divide by the number of partitions used...
amistre64
  • amistre64
the more subdivision of your interval, the more accurate your average f(x) will be
anonymous
  • anonymous
f(x)=sqrt(25-x^2)
amistre64
  • amistre64
what the integral does is divides the interval into an infinite number of peices then adds them all up to get an exact value ;)
anonymous
  • anonymous
the interval is 1<=x<=5
amistre64
  • amistre64
do you want integration? or the slower way like trapaziodal rule?
anonymous
  • anonymous
probably integration
amistre64
  • amistre64
yeah...probably :)
amistre64
  • amistre64
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:
amistre64
  • amistre64
[S] 5cos(t) dt -> 5sin(t) +C but since we got and interval we can forgo the +C part.
amistre64
  • amistre64
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 ;)
amistre64
  • amistre64
thats my mistake....sqrt(1-sin^2) = cos^2...not cos; got it:)
amistre64
  • amistre64
....nah, I was right to begin with....if you got a show you can watch, now would be the time to do it ;)
amistre64
  • amistre64
This is what I get for the area 978.338522 and Im like 67% sure im right lol
amistre64
  • amistre64
yep, 98% sure 978.338522

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