I think the only way is to use method of iteration.
EDIT: Or the equation can be rewritten as . Draw the curves and on same graph paper; the first point of intersection on the right of the origin will be your answer.
Find the coordinates of the first inflection point to the right of the origin:
I think that it's obvious that I have to find the second derivative of Si(x) and then set it equal to zero. Here is what I did:
Let
(according to FTC1)
Assuming all is well to here (big assumption, I know), I get stuck on solving for zero:
When I graph this on my calculator, there isn't an obvious solution.
For whatever it's worth, my calculator tells me that the answer to this is approximately
Anybody see where I am going wrong or have a suggestion to get me unstuck?
Thanks.
OK, I've worked this problem out and have determined that the x-coordinate of the inflection point is 4.4934 (using Newton's method). Now I need to evaluate Si(4.4934).
I'm applying FTC2 to find this answer:
Let
Then, if I can determine F(x), I should be able to find Si(4.4934) = F(4.4394) - F(0). But I don't know how to do this (other than with a calculator).
What do I do? Thanks.