View Single Post
P: 76

## 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:

$$2 \int_{0}^{1} |x| - (x^2 - 1) \delta x = 2\left[\frac{|x^2|}{2} - \frac{x^3}{3} + x\right]_{0}^{1}$$
$$= 2\left[\frac{1}{2} - \frac{1}{3} + 1\right]$$
$$= 2\left[1 \frac{1}{6} \right] = 2\frac{1}{3}$$

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