Question

when it comes to finding areas under two graphs and we are given a certain x-interval,do we always have to find the intersection points?
will i get the same answer if i dont find the intersection points?

Answer 1

if two graph intersect @ given points or beyond the interval - no problem; you'll get the same answer.
what if the same graphs intersect with each other "inside your interval" & may even cancel each other?
I always try to find inset section points - it helps me understand graphs behavior inside the given interval.

Answer 2

but im doing this in calculus where i will have to intergrate too

Answer 3

I would find intersection points anyway, unless you know for sure that graphs are "stable" inside given interval

Answer 4

yeah you have to find the intersectin points to determine the area between two graphs
if you find the individual areas of the graph your answer would be bigger than expected value

Answer 5

You asking the wrong questions. The point is find the point of intersection if it is necessary to get your answer.

Answer 6

ohk but this wont help in areas in calculus

Answer 7

let's try to do an example - easier to see :)

Answer 8

you have to put the value of definite integrals individually in the respective functions and subtract them.

Answer 9

ok throw it to us or lets try mine, y=x^4-2x^2 and y=2x^2

Answer 10

points of intersections are: x= +/- 2 & y=8
rght?

Answer 11

so, area A=\[\int\limits_{-2}^{2} (x ^{4}-2x ^{2} -2x ^{2})dx = ..\]
solve it

Answer 12

points of intersection are correct but we should also consider x=0

Answer 13

why...?

Answer 14

A=128/5
am i right?

Answer 15

wait

Answer 16

im getting zero

Answer 17

let's see

Answer 18

\[=x ^{5}/5 - 4x ^{3}/3\] from (-2) to 2
=32/5 -32/3 - (-32/5+32/3) = 64/5 - 64/3 = -128/5
"-" could be omitted...area

Answer 19

oh i see. so i can do a direct substitution...and get the same result? ok thanx

Answer 20

:)

Answer 21

my professor always said we shouldn't be worried which function subtracted from which - no difference to the numerical result, just be aware of sign.
Just a helpful hint

Answer 22

thanx we were told the same