The discussion revolves around solving an integral involving a square root in the denominator, specifically the integral of the form \(\int_{0}^{a}\frac{s \ ds}{\sqrt{y^{2} + s^{2}}}\). Participants are seeking clarification on the steps taken to evaluate this integral and the reasoning behind the use of substitutions.
The discussion is ongoing, with participants sharing their attempts and seeking further clarification on the substitution method. There is an acknowledgment of the need for practice in recognizing when to apply specific techniques, but no consensus has been reached on the best approach.
Participants are grappling with the concept of substitution in integrals and the conditions under which it is applicable. There is a mention of the importance of practice in developing intuition for these types of problems.
It seems to me that an ordinary substitution was used: u = y2 + s2, du = 2s ds.Taturana said:Homework Statement
I need to proceed to solve this integral:
Homework Equations
[tex]\int_{0}^{a}\frac{s \ ds}{\sqrt{y^{2} + s^{2}}} = \left [ \sqrt{y^{2} + s^{2}} \right ]_{s=0}^{s=a}[/tex]
The Attempt at a Solution
I don't understand what he did from the left-hand side of the equation to the right-hand side... could someone explain me, please?
Thank you,
Rafael Andreatta
Mark44 said:It seems to me that an ordinary substitution was used: u = y2 + s2, du = 2s ds.
Taturana said:I tried some math here and I still don't understand...
Taturana said:When you get an integral of that type, how do you know when you need to make this kind of substitution?
Show us what you're trying and we'll straighten you out.Taturana said:I tried some math here and I still don't understand...
When you get an integral of that type, how do you know when you need to make this kind of substitution?
Could you explain me more clearly?
Thank you very much...