#$&*
Mth174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
How can i use SIMP(n) to estmate arc lenghth of f(x)on interval [a,b]?
And how to find the indefinite intergral of 1/(a^2 + x^2)
@& To get the arc length of the graph you have to first know what the approximate arc distance is on a short interval.
Consider an small interval of length `dx, with the point x_sample somewhere within that interval.
Consider the thin trapezoid formed between the graph and the x axis.
What is the expression for the slope of the graph above the point x_sample?
Why do we say that the slope of the trapezoid is close to the slope at x_sample?
Between the graph point on the left side of the interval and the graph point on the right, what is the run, and what is the rise (as determined by the slope at x_sample)?
What therefore is the distance between these points?
Tell me also what you know about Simpson's Rule.
*@
@& 1 / (a^2 + x^2) = 1 / (a^2 ( 1 + (x / a)^2).
If you let u = x / a then du = dx / a and your integrand becomes
(1 / a) * (1 / (1 + u^2)).
Compare this to the derivative of tangent(u) and you will find your antiderivative.
*@
@& Please see my notes on the second question, which I believe you will understand well.
Then see if you can answer the questions I pose in response to your first question. Once I see your answers I will know what to tell you next.
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you. &#
*@