Calculating integrals of area between two functions, involving absolute values...
Thank you very much, guys. Nice to hear that you can solve integrals by looking for symmetry! This I wasn't aware of.
Gregg, I tried your first integral and I didn't get the same answer as you. Your second integral I understand perfectly though.
Looking closer, it seems you wrote the first integral out incorrectly. I believe it should be this:
[tex]
2 \int_{0}^{1} x  (x^2  1) \delta x = 2\left[\frac{x^2}{2}  \frac{x^3}{3} + x\right]_{0}^{1}
[/tex]
[tex] = 2\left[\frac{1}{2}  \frac{1}{3} + 1\right] [/tex]
[tex] = 2\left[1 \frac{1}{6} \right] = 2\frac{1}{3} [/tex]
I truly do appreciate your assistance. This ability to solve using symmetry is quite remarkable, but I suppose it really isn't much of a surprise: symmetry is useful in so many areas in mathematics!
Cheers,
Davin
