February 14th, 2019, 10:46 PM |
#1 |

Newbie Joined: Feb 2019 From: United Arab Emirates Posts: 1 Thanks: 0 | *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 |

February 15th, 2019, 07:57 AM |
#2 |

Global Moderator Joined: Dec 2006 Posts: 20,759 Thanks: 2138 | |