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 QUESTION: I want to integrate the following function:∫(2x3 – 3x2 + 5x – 2)dx and ∫(5sin2θ + 2cos4θ)dθ. Through self study I have worked out that they are 0.5x^4 + x^3 + 2.5x^2 – 2x + C and -5/2cos2θ + 0.5sin4θ+C. I would appreciate it if you could confirm my answers and/or correct them, please. Thank you, kind regards, Mike
ANSWER: The polynomial was done OK.
The trig problem was done OK.
Both look OK.
To see if the answers are correct, take the derivative.
The derivative of x^4/2 + x^3 + 5x^2/2 - 2xc + C
is 2x^3 + 3x^2 + 5x - 2, which is what was given to be integrated.
The derivative of -2.5cos2Θ + 0.5sin4Θ + c
is -2.5(-sin2Θ)2 + 0.5(cos4Θ)4 = 5sin2Θ + 2cosΘ,
which is what we given to be integrated.
---------- FOLLOW-UP ----------
QUESTION: Can I enter equations in a spreadsheet (excel etc) to find a derivative or integral, please? For instance I have the equation for the instantaneous voltage during the charge of a capacitor, viz v=V(1-e^t/T)where I know the values of t and T and V. Kind regards and thanks for last encouragement. Mike
Answer You can't find the derivative of integral, but only a numerical approximation. For derivatives, use a very small difference in x values to find the y value. For integrals, use very small x values between the low point and high point and find the area of the rectangles between each of the points. The height would be the value of the function and the width would be the difference in the x's for each interval. The sum of the areas of all the rectangles would be the derivative.
The derivative of e^t is e^t.
Here, the derivative of V((1-e^t)/T) is (V/T)(-e^T).
For new questions it is better to send it as a new question rather than a follow up.
