- #1
Silva_physics
- 10
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Hi! Could anybody, please, help me with integrate this: Integrate[ (|x| / x) dx]
Thank you:)
Thank you:)
Silva_physics said:Ok, thanks, I thought about it, so in the cases x>0,x<0 it is 1 and in x=0 it is 0, that's all?
NO! For x> 0 |x|/x= x/x= 1 but for x< 0, |x|/x= -x/x= -1. At x= 0 it is undefined.Silva_physics said:Ok, thanks, I thought about it, so in the cases x>0,x<0 it is 1 and in x=0 it is 0, that's all?
Integration is a mathematical process used to find the area under a curve. It involves finding the antiderivative of a function and evaluating it at specific bounds.
To integrate absolute value functions, you can split the function into two parts, one for when the input is positive and one for when it is negative. You can then use the definition of integration to evaluate each part separately.
Yes, an example of integrating |x|/x is ∫|x|/x dx. By splitting the function into two parts, we get ∫x/x dx when x is positive and ∫-x/x dx when x is negative. Simplifying these expressions gives us ∫1 dx and ∫-1 dx, which evaluate to x and -x, respectively. Therefore, the overall integral is x + C when x is positive and -x + C when x is negative.
The constant of integration, denoted as C, is added to the result of an indefinite integral to account for all possible antiderivatives of a given function. It represents the family of curves that the original function belongs to.
You can check your integration solution by taking the derivative of the antiderivative you found and comparing it to the original function. If the derivative matches the original function, then your integration solution is correct.