Question

integrals...area under the curve?

Answer 1

Gowlet

Answer 2

yeah, what about em?

Answer 3

how do we do them...without any rule?

Answer 4

well if you wanna live by no rule, then it doesnt matter HOW you do them ;)

I gotta ask, what do you mean?

Answer 5

we have a curve with a grid...we need to count the squares and find the area under the curve

Answer 6

is there any more accurate way to do this than to simply count the squares?

Answer 7

then you just gotta do your best guess...

the area of a "trapazoid" is:

(base)([height rightside + height leftside] /2) right?

Answer 8

oh ok thanks i have another question

Answer 9

how would i find the average value of f(x) over an interval?

Answer 10

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

Answer 11

how big is the interval?

Answer 12

the average f(x) is the number of each partition added together; then divide by the number of partitions used...

Answer 13

the more subdivision of your interval, the more accurate your average f(x) will be

Answer 14

f(x)=sqrt(25-x^2)

Answer 15

what the integral does is divides the interval into an infinite number of peices then adds them all up to get an exact value ;)

Answer 16

the interval is 1<=x<=5

Answer 17

do you want integration? or the slower way like trapaziodal rule?

Answer 18

probably integration

Answer 19

yeah...probably :)

Answer 20

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:

Answer 21

[S] 5cos(t) dt -> 5sin(t) +C but since we got and interval we can forgo the +C part.

Answer 22

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 ;)

Answer 23

thats my mistake....sqrt(1-sin^2) = cos^2...not cos; got it:)

Answer 24

....nah, I was right to begin with....if you got a show you can watch, now would be the time to do it ;)

Answer 25

This is what I get for the area 978.338522 and Im like 67% sure im right lol

Answer 26

yep, 98% sure 978.338522