Dealing with absolute value functions

AI Thread Summary
To find the integral of the difference between the functions f(x) = |x-2| and g(x) = x^2 + 2x, it's essential to address the absolute value in f(x). The discussion suggests simplifying g(x) - f(x) but raises concerns about handling the absolute value correctly. A recommended approach is to evaluate the problem in two scenarios: when the expression inside the absolute value is positive and when it is negative, applying a negative sign as needed. This method ensures a comprehensive understanding of the function's behavior across different intervals. Properly managing the absolute value is crucial for accurate integration.
sunfleck
Messages
6
Reaction score
0
In order to get an integral I need to find the difference between two functions, but I'm not sure how to deal with the absolute value...


f(x) = \left|x-1-1\right|
g(x) = x^2 + 2x

g(x) - f(x) = (\left|x-1\right|-1) - (x^2 + 2x)
=...
I don't know if I can simplify it anymore... can I take that |x| out so - 2x + |x| = - x? If so what happens to the |-1| I feel like I probably can't simplify any further, but I'd like to know for sure
 
Physics news on Phys.org
The easiest way I find to solve problems like this is to solve the problem twice - once where the contents of the modulus are positive anyway, and once when they're negative (in which case you need to put an extra minus sign in front of them).
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Solve ##\left| x+3 \right|= \left| 2x+1\right|##
Replies
7
Views
3K
How Do You Solve Complex Absolute Value Inequalities?
Replies
4
Views
2K
Need help in manipulating rational absolute value inequalities
Replies
11
Views
2K
Absolute Value (algebraic version)....1
Replies
2
Views
1K
Absolute Value (algebraic version)....2
Replies
7
Views
2K
Confusion about ##\sqrt{x^2}= \left| x \right|##
Replies
1
Views
2K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
Replies
8
Views
3K
Solving an equality with absolute values
Replies
10
Views
2K
Solving an absolute value quadratic inequality
Replies
9
Views
2K
Doubt solving a polynomial inequality
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top