Evaluate the definite integral of the algebraic
function. Use a graphing utility to verify your result. Usually you can plug in for the variable with the limits but I'm not really sure how to approach this. I'm learning calc online and I feel like I have a poor grasp of this topic.

Question

Evaluate the definite integral of the algebraic
function. Use a graphing utility to verify your result. Usually you can plug in for the variable with the limits but I'm not really sure how to approach this. I'm learning calc online and I feel like I have a poor grasp of this topic.

anonymous · Answer

$$\int\limits_{2}^{7} 3dv$$

mathmale · Answer

First of all, I'd suggest you remove the constant coefficient 3 from the given inegral, to obtain $$3\int\limits\limits_{2}^{7} dv.$$

mathmale · Answer

At this point you could either accept the fact that $$\int\limits_{}^{}dv = v + C,$$...or we could discuss why this is so.

$$\int\limits\limits_{}^{}dv = v + C,$$is an "indefinite integra," because no limits of integration are given.  If we move on to the given definite integral, we end up with$$3\int\limits_{2}^{7}dv=3v~fro~v=2~\to~v=7=7-2+?$$

mathmale · Answer

If you feel you have a 'poor grasp of this topic,' please choose any area of this topic that you'd like to discuss right now so that the current math problem will be clearer to yuo.

mathmale · Answer

The last equation I typed should be$$3\int\limits\limits_{2}^{7}dv=3v~fro~v=2~\to~v=7=7-2=~??$$

anonymous · Answer

I guess what I don't quite understand is the process of evaluating integrals or what the purpose of it is/what the evaluation yields. Thank you very much for your help.

anonymous · Answer

Is the evaluation you gave because of the fundamental rule of calculus?

mathmale · Answer

Purpose:  definite integrals are perfectly suited to finding "areas under curves" between two limits.   For example, in the problem you're working on right now, the function is y=3, and you are looking to find the area under this curve (actually, a straight line) between x=2 and x=7.  were you to draw this, you'd find that the area is 15, which should the exactly the same as the result of the definite integral you're working on right now.

The indef. integral is a mathematical operation which is the opposite of differentiation.

Supposing you have f(x)=x^3; were you to take the first derivative of this, you'd get f'(x)=3x^2.  supposing you wanted your original function back, you could get it back b y integrating 3x^2 with respect to x.

Of course there's more involved, but this info is basic to understanding what definite and indef integrals are.

anonymous · Answer

Thank you very much. I understand much better now.

mathmale · Answer

to answer your question: Please see http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus Specifically, please see this excerpt from that site:

mathmale · Answer

do let me know if and when you have further questions.  You could alwyas "tag" me when you post a new question.  If I'm on OpenStudy, i'd be glad to help you.  Best wishes!

anonymous · Answer

Thanks again!