Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
Post a reply
Topic review (newest first)
If you mean e^x^2, then you're going to love this one. There is an antiderivative of e^x^2. But we can't integrate it. There is a function of it's antiderivative, but it was a function that was unknown until we were investigating the antiderivative of e^x^2. Here is an example you will understand:
That is the defintion of ln(x). The same thing happens when you take the integral of e^x^2. The function is defined by that integral.
Correct me if I'm wrong, but isn't it this?
I think you're thinking of ex².
Anyway, every function can be integrated, it's just that not all of them can be integrated algebraically.
If you wanted to find ∫ex²dx, you'd need to take each and every real value of x and work out the integral at that point using numerical methods. I'd advise telling a computer to do it.
Just read about this today. It stated that every continuous function has an antiderivative. My book then trailed off on something about integreting with a constant as the lower limit of integration. In the end I couldn't see there point, and they then simply said "we state the theorem without proof:"