Question

Finding interval for area inside one loop of the lemniscate.

Answer 1

i am not sure how to find the interval of the integral, 0 to pi/2 does not work( times 2), 0 to pi does not work

Answer 2

think about an interval for t where cos(t) ranges from 0 to 0

Answer 3

at what values of t is cos 0 ?

Answer 4

pi/2 and 3pi/2

Answer 5

yes, but in that interval cos is negative
try another

Answer 6

5pi/2

Answer 7

right, or if you are allowed to use negative angles -pi/2 to pi/2

Answer 8

or should i use -pi/2 to pi/2

Answer 9

-pi/2 to p/2 works, but think about the other possibility that I didn't hand you
what is wrong with pi/2 to 5pi/2

Answer 10

?

Answer 11

who that make the integral 0?

Answer 12

wont*

Answer 13

yeah, hmmm let me think for a sec
funny I feel more comfortable with double integrals in polar than single

Answer 14

sin is just ruining this problem

Answer 15

I honestly have never seen a single integral in polar before
do you have a source of info I can look at? all I can find online is double integral stuff...

Answer 16

hmm, no it is just an example from my practice exam, the answer is 7/2 just no clue what the interval is

Answer 17

ok found this
http://en.wikibooks.org/wiki/Calculus/Polar_Integration

Answer 18

I guess the logical thing to do is split the integral up into two and use absolute value

Answer 19

-pi to pi?

Answer 20

but that would give us the other half of the lemniscate, and will also integrate to 0