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justinfung
Group Title
solving for g'(x) when g(x)=integral from sqrt(x) to x^2, (sin t)(sqrt t) dt
 one year ago
 one year ago
justinfung Group Title
solving for g'(x) when g(x)=integral from sqrt(x) to x^2, (sin t)(sqrt t) dt
 one year ago
 one year ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
derivative of the integral is the integrand, plus chain rule replace \(t\) by \(x^2\) and multiply by the derivative of \(x^2\) get \[\sin(x^2)\sqrt{x^2}\times 2x\] for the top part bottom part is the same, but make it negative
 one year ago

justinfung Group TitleBest ResponseYou've already chosen the best response.0
I think I am suppose to break it up. integral from sqrt x to 0 plus 0 to x^2. But i have no idea why this is the way to do it
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yes but you can break up anyway you like
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the top part gives what i wrote above, the bottom part is analogous, just make it negative
 one year ago

justinfung Group TitleBest ResponseYou've already chosen the best response.0
the bottom can be any number??
 one year ago

justinfung Group TitleBest ResponseYou've already chosen the best response.0
I know I'm suppose to use the second fundamental theorem
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yes \[\int_{\sqrt{x}}^{x^2}f(t)dt=\int_{\sqrt{x}}^af(t)dt+\int_a^{x^2}f(t)dt\]
 one year ago

justinfung Group TitleBest ResponseYou've already chosen the best response.0
My teacher chose 0 though. Is there a reason for that? should I just choose 0 everytime?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
take the derivative of the second part, get \(f(x^2)\times 2x\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the derivative of the first part is \(f(\sqrt{x})\times \frac{1}{2\sqrt{x}}\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if you like to pick zero, go ahead a pick zero makes no difference
 one year ago

justinfung Group TitleBest ResponseYou've already chosen the best response.0
Ok I understand it now. Thanks!!!! :)
 one year ago
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