Sketch the region enclosed by y= 6|x| and y = x^2 -7

[apiwowar]

i know that the way to solve this is by evaluating the integral from a to b of the first function minus the second one but how would i solve for x to find out what the limits of integration should be?

if you set them equal to each other you get 6|x| = x^2 - 7
but I am not exactly sure what to do with the |x|

 

[rootX]

Could you graph both functions ...
http://www.padowan.dk/graph/
but even without, you can take two cases x>=0, x<0 .. and solve them

 

[greenpick]

like rootX said, when dealing with absolute value functions, it's usually best to define it peace-wise.

f(x) = 6x for x >= 0
-6x for x < 0

Or you could notice that the two functions are even, and you could thus solve for x using 6x, and keep in mind that there is another intersection point opposite the y-axis.

 

[HallsofIvy]

i know that the way to solve this is by evaluating the integral from a to b of the first function minus the second one but how would i solve for x to find out what the limits of integration should be?

if you set them equal to each other you get 6|x| = x^2 - 7
but I am not exactly sure what to do with the |x|

If $x\ge 0$, |x|= x so this is 6x= x^2- 7 which is the same as x^2- 6x- 7= 0.

If x< 0, |x|= -x so this is -6x= x^2- 7 which is the same as x^2+ 6x- 7= 0.