Calc 2 using washer meathod v.s cylindrical shells

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The discussion focuses on the comparative advantages of the washer method versus the cylindrical shells method for calculating volumes in calculus. While cylindrical shells are often considered easier to apply, there are scenarios where the washer method may be more appropriate or simpler. The choice between the two methods can depend on the specific problem being solved. Participants highlight that each method has its own strengths and weaknesses based on the geometry of the region being analyzed. Ultimately, the decision on which method to use can vary from problem to problem.
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What are the reasons for using washer meathod v.s cylindrical shells?

Cylindrical shells are much easier but there has to be some reason we can always use them

Thanx
 
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carlosgrahm said:
What are the reasons for using washer meathod v.s cylindrical shells?

Cylindrical shells are much easier but there has to be some reason we can always use them

Thanx

Hi carlosgrahm! :smile:

(i assume you're talking about finding a volume by integrating)

Sometimes one is easier, sometimes the other. :smile:

Do you have a specific problem in mind?
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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