AboutScotto Expertise Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.).
I also have answered some questions in
Physics (mass, momentum, falling bodies),
Chemistry (charge, reactions, symbols, molecules), and
Biology.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications Maybe not a publication, but I have respond to well oveer 3000 questions on the PC.
That's around 2,000 in basic math and 1,000 in advanced math.
Education/Credentials I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients My past clients have been students at OSU, students at the college in South Seattle,
referals from a company, friends and aquantenances, people from my church, and people like you.
Question How do you evaluate this definite Integral : Integral of (x^2)*e^(-x^2) with limits from 0 to 1?
I tried to use the following technique but I could not do it:
letting u = x^2, du = 2xdx
1/2du = xdx;
substituting everything back is where I got stuck.
Answer Let u=x, so du=dx and dv=xe^(-x²), so v=e^(-x²)/2.
This problem fits in with the u-v problems where
the integral(udv) = uv - integral(vdu).
Integral(vdu) = integral(e^(-x^2)/2) from 0 to 1. This integral is almost the normal distribution, which can’t be integrated with bounds on it. The variables σ and µ are 1 and 0, respectively. The only difference between that and a normal distribution is that the normal distribution is divided by √(2π). Find the values on the normal table at 1 (that value a 0 is 0) and multiply by √(2π) to get the result of the integration.
Once you have this value, subtract it from e^(-1/2) (our uv) to get the final answer.
