Calculus Calculus Math Forum

February 14th, 2019, 11:46 PM   #1
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*I need help with this problem*

Hello everyone,

So I started a mathematics research in calculus.
I was trying to find which quadratic equation that goes through point A(-5,5) and B(5,5) would give the minimum surface area of revolution.
As the general formula of a quadratic function is
f(x)=ax^2+bx+c
After putting A and B into the general formula, I found that f(x)=ax^2-25a+5 would be the general formula for the quadratic equations that pass the two points.
Using the surface area of revolution formula
I ended up at following expression (check attachment please)

So if i solved the definite integral above it would give me an expression in a and then dA/da=0 and d^2A/da^2>0 would give me the a value at which the surface area is the minimum right?
However, the integration became too complicated and that is where I'm stuck.
I did get the answer to that integral but differentiating that again is overwhelming.
So, I'm asking if there was a way to simplify the method or the calculation.

Thanks,
Josh
Attached Images Screen Shot 2019-02-15 at 11.13.01 AM.jpg (9.7 KB, 3 views) February 15th, 2019, 08:57 AM   #2
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Quote:
 Originally Posted by sangbeompark13 . . . would give the minimum surface area of revolution.
When what part of the parabola is rotated through what angle about what line? Tags calculus, differentiation or curve, integration, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

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