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About Scotto
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.

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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.

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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.

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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.

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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).

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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.

 
   

You are here:  Experts > Teens > Homework/Study Tips > Calculus > calculus

Calculus - calculus


Expert: Scotto - 7/3/2008

Question
calculate the area between the curves(transedental):
1.f(x)=2sin(x)   g(x)=tan(x)
2.f(x)=2sin(x)+sin(2x)
3.f(x)=x^3-x^2=-x^2+9

Answer
The curves given are
1.f(x)=2sin(x)   g(x)=tan(x)
2.f(x)=2sin(x)+sin(2x)
3.f(x)=x^3-x^2=-x^2+9

I am given no endpoints for any of them.  On 1, it might be where the cross.  On 2 and 3, it might where they intersect the x axis.

Anyway, the integrals are (taking I as integral):
I(2sin(x)) is -2cos(x)+C, I(tan(x))=sec˛(x)+C, I(2sin(x)+sin(2x))=
-2cos(x)-cos(2x)/2, and I(-x˛+9) is -x^3/3 + 9x + C.

The C's will drop out when the endpoints are known.  If the top endpoint is b and the lower endpoint is a, the answer is I(b)-I(a).

By the way, the proper spelling of transedental is transcendental.

Here is a definition, taken out of the form
//mathworld.wolfram.com/TranscendentalNumber.html :
"A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real transcendental number must also be irrational, since a rational number is, by definition, an algebraic number of degree one."

The only transcendental numbers that I know of with a name are e and pi, but there are infinitely many of them.

I'm not sure that was what was meant when the term was used.


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