The discussion revolves around solving the definite integral ∫|x^3-x|dx from -1 to 2, focusing on the challenges posed by the absolute value in the integrand. Participants explore how to determine the intervals where the expression inside the absolute value is positive or negative, and how to approach the integration process step by step.
Participants generally agree on the zero points of the function and the need to analyze the function's behavior across different intervals. However, there is no consensus on the best approach to proceed with the integration, as some participants express confusion and seek clarification.
Participants mention the need for visual aids and the exploration of symmetry, indicating that the discussion is still developing with respect to the integration process and the handling of absolute values. Some assumptions about the function's behavior may not be fully explored.
The modulus sign! I In which limit I have to take positive and negative in the modulus I could not understand!Krylov said:
Well I am not able to draw precisely and that is where the problem lies !BvU said:
well kindly please tell me the terminal points ! I found it as -1,0 and 1 am I correct??BvU said:Doesn't have to be precise. Simply investigate the function a little.
Where it comes from on the left, where it goes through zero and where it goes to on the right.
Perhaps there is even a little symmetry to explore and make good use of ...
but the zero points of ##\ \ x^3-x = x(x+1)(x-1) \ \ ## are indeed -1, 0, 1 .Thanks I finally got that !Thank you very much !BvU said:I don't know what terminal points are
Between -1 and 0 two out of three factors are < 0 and the other is > 0, so the expression is positive.
Between 0 and 1 ...
There is antisymmetry : ##\ \ (-x)^3 -(-x) = -(x^3 - x) ##, so ...
