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

  • Thread starter Thread starter apiwowar
  • Start date Start date
  • Tags Tags
    Sketch
apiwowar
Messages
94
Reaction score
0
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|
 
Physics news on Phys.org
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.
 
apiwowar said:
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.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top