- #1
Telemachus
- 835
- 30
Homework Statement
I must solve [tex]\displaystyle\int_{}^{}x|x|dx[/tex]
How should I proceed?
Quantumjump said:You just distinguish the two cases x>=0 or x<0 and then teh calculation is straighforward. in the first case you wil have the integral of x*x and in the second you will have the integral of -x*x
Are you serious?The Chaz said:I wonder why Hurkyl didn't just say that in his reply... hmm...
I guess he doesn't know how to do it...
Unit said:Are you serious?
LCKurtz said:Just guessing here, but I would say obviously no, he isn't serious. Rather it is a gentle jab at quantumjump for not giving the OP a chance to think for himself.
The indefinite integral of x|x|dx is equal to (1/3)x^3 + (1/4)x^4 + C, where C is the constant of integration. This can be found by using the power rule for integration and substituting x|x| for u.
The process for solving the definite integral of x|x|dx involves finding the indefinite integral first, then plugging in the upper and lower limits of integration and subtracting the results. This will give you the value of the definite integral.
Yes, substitution can be used to solve x|x|dx. You can substitute u = x|x| and then use the power rule for integration to find the indefinite integral.
No, there is no shortcut method for solving x|x|dx. The process of finding the indefinite integral and plugging in the limits of integration is the most efficient way to solve this integral.
Yes, you can use integration by parts to solve x|x|dx. However, it will involve multiple steps and may not be the most efficient method. It is recommended to use substitution or the power rule for integration instead.