Question

Calculus Area Between Curves!!!!

Answer 1

suppose f(x) > g(x) in the given interval, then area between f(x) and g(x) :
\[\large A = \int\limits_a^b f(x) - g(x) ~~dx\]

Answer 2

regardless of < or > ....
\[\large A = \left|\int\limits_a^b f(x) - g(x) ~~dx\right|\]

Answer 3

therefore 'finding which is on top' is fairly redundant

Answer 4

hmm if we don't look for top/bottom, the mods should be kept inside integral right ?

Answer 5

I was able to split it up into three separate integrals where it was positive, negative etc but again i may have got lost along the way

Answer 6

the integration creates a number ... it is the absolute value of the integration results that we are after instead of running into tachyon issues

Answer 7

not positive negative i mean top and bottom haha been a long day

Answer 8

trachyon? terriddle? some absolute value property