Question

sketch the region bounded by the graphs of the given functions and find the area of the region
y = x^4 - 2x^2; y = 2x^2

Answer 1

x^4 - 4x^2 = 0
x = -2, x = 0, x = 2
interval [-2, 2]

Answer 2

\[A=\left| \int\limits_{-2}^{2}[(x^4 - 2x^2) - (2x^2)]dx \right|\]

Answer 3

I am thinking that it is symmetrical so perhaps a = 0 and b = 2
then constant 2 of the integral

Answer 4

I always resort to absolute value so I wouldn't have to figure out which function is greater

Answer 5

I am not sure if that will give me trouble in the long run

Answer 6

what you have done so far seems correct although I have never seen this absolute value thing

Answer 7

Lemme just recheck what you have done. Give me a few mintes

Answer 8

Okkk Firstly x^2 is greater than x^4-2x^2
So subtract x^4-2x^2 from x^2 and remove the absolute value

Answer 9

you plugged in the values?

Answer 10

I graphed it and it was quite apprent

Answer 11

secondly we can use your symmetry rule and set up the equation like you suggested

Answer 12

see graphing sometimes takes a lot of time so I use the absolute value I thought it saves me 3-5 minutes just to figure out which function is greater
I just want to make sure that this laziness will not bite me in the arse during exam

Answer 13

Yaaaa im wondering that tooo

Answer 14

What we can do is try out a few examples and see what happens

Answer 15

I have tried it on almost 20 examples already and they seem to be fine

Answer 16

Intuitively it should be fine

Answer 17

\(\large A=\int\limits_{-2}^{2}\Big| [(x^4 - 2x^2) - (2x^2)]\Big| dx \)

Answer 18

ganeshie agrees :)

Answer 19

that is reassuring

Answer 20

keeping the absolute value outside gives us problems later...

Answer 21

when.. the two curves cross each other multiple times in the given interval...