Summation by Steps: Calculus Self-Teaching Homework Help

[bobie]

Homework Statement

I hope this is the right forum for this question.
I am starting to self-teach calculus, could you help me shape my problem?
I am trying to use wolfram:
I know that if I integrate an equation say: 5/\sqrt x, I will get the area underneath that curve
http://www.wolframalpha.com/input/?i=+integrate+y=+5/sqrt(x)+++from+20+to+10^4

Now, I want to summate all the values we get increasing x by x or another value:
5/sqrt20 +5/sqrt40...+5/sqrt 10^4

What do you call this operation? is it still integration, by steps or what?
is it necessary to regulate dx to 20, or what
Can you help me formulate this operation :
integrate y = 5/sqrt x from 20 to 10^4 , step 20 or x or...

THanks for your help

Homework Equations

The Attempt at a Solution

 

[Fightfish]

What you are trying to do is just discrete summation. In integration (as interpreted in the Riemann summation sense), the width of the "boxes" that you have divided the area under the curve into approaches infinitely small.

The best way to write your desired operation is simply
\sum_{i = 1}^{500}\frac{5}{\sqrt{20i}}

You could of course, multiply this by another factor of 20 if you want to obtain some sort of "area estimate" through finite-sized boxes.

 

[bobie]

The best way to write your desired operation is simply
\sum_{i = 1}^{500}\frac{5}{\sqrt{20i}}

You could of course, multiply this by another factor of 20 if you want to obtain some sort of "area estimate" through finite-sized boxes.

Thanks, can you tell me how to tell that to wolfram?

 

[Fightfish]

Wolfram is highly versatile, and there are plenty of help options. But just to give you a quick overview of the syntax, it goes like:

Sum [ func, {counter variable, start value, end value}]

 

[bobie]

Wolfram is highly versatile, and there are plenty of help options. But just to give you a quick overview of the syntax, it goes like:

Sum [ func, {counter variable, start value, end value}]

Probably I messed it up, but there is a variable in the result and I didn't get a single value, can you fix it?
http://www.wolframalpha.com/input/?i=sum+[+5/sqrt(k+x),{k++,+1,+10}]

 

[Fightfish]

This is because you had an undefined variable, x. For your example above, you want to choose x = 20 to reproduce the series.
http://www.wolframalpha.com/input/?i=sum+[+5/sqrt(20k),{k++,+1,+500}]

 

[bobie]

Thanks, that's it.

 

[bobie]

Hi,
it seems impossible to use decimal figures, or is there a particular grammar?
Must the step be an integer , or is it possible to increase the value by a decimal , say by 1/10?
Thanks