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anonymous
 one year ago
find F'(x) when F(x)= integral from 4 to x^2 (2 sqrt(1+t^3) dt)
anonymous
 one year ago
find F'(x) when F(x)= integral from 4 to x^2 (2 sqrt(1+t^3) dt)

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[F(x)=\int\limits_4^{x^2} g(t) dt=G(t)_4^{x^2}=G(x^2)G(4) \\ \text{so we have } F(x)=G(x^2)G(4) \\ \text{ differentiate both sides }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[F'(x)=(x^2)'g(x^2)0 \text{ by chain rule and constant rule }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2@aawowaa are you there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, I'm going over it.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you understand that g(t) is 2sqrt(1+t^3)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2And that I was using G(t) to represent the antiderivative of g(t) that is G'=g

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now I plug in 2sqrt(1+t^3) back?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2g(t)=2sqrt(1+t^3) so g(x^2)=?"

freckles
 one year ago
Best ResponseYou've already chosen the best response.2ok so that is what you replace g(x^2) with

freckles
 one year ago
Best ResponseYou've already chosen the best response.2don't forget to find (x^2)' which is next to g(x^2)
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