- #1
zmalone
- 10
- 0
I understand [itex]\int[/itex][itex]^{1}_{-1}[/itex]1-|x|dx = 1 visually just by graphing it and taking the area of the triangle but for the sake of more complicated examples I'm not exactly sure what step I'm messing up when I use the FTOC:
|x|= x when x>0, -x when x<0
[itex]\int[/itex][itex]^{0}_{-1}[/itex]1-|x|dx + [itex]\int[/itex][itex]^{1}_{0}[/itex]1-|x|dx
= [itex]\int[/itex][itex]^{0}_{-1}[/itex]1-(-x)dx + [itex]\int[/itex][itex]^{1}_{0}[/itex]1-(x)dx
= [itex]\frac{x^2}{2}[/itex]|[itex]^{0}_{-1}[/itex] - [itex]\frac{x^2}{2}[/itex]|[itex]^{1}_{0}[/itex]
= -1/2 - 1/2 = -1 [itex]\neq[/itex]1
Any input is appreciated and hope this makes sense lol (still getting used to the formula drawer).
|x|= x when x>0, -x when x<0
[itex]\int[/itex][itex]^{0}_{-1}[/itex]1-|x|dx + [itex]\int[/itex][itex]^{1}_{0}[/itex]1-|x|dx
= [itex]\int[/itex][itex]^{0}_{-1}[/itex]1-(-x)dx + [itex]\int[/itex][itex]^{1}_{0}[/itex]1-(x)dx
= [itex]\frac{x^2}{2}[/itex]|[itex]^{0}_{-1}[/itex] - [itex]\frac{x^2}{2}[/itex]|[itex]^{1}_{0}[/itex]
= -1/2 - 1/2 = -1 [itex]\neq[/itex]1
Any input is appreciated and hope this makes sense lol (still getting used to the formula drawer).