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anonymous
 4 years ago
If the average rate of change of F on [1,3] is k, find
∫sin(t^2) dt [1,3] in terms of k
anonymous
 4 years ago
If the average rate of change of F on [1,3] is k, find ∫sin(t^2) dt [1,3] in terms of k

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JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1...you mean where \[ F(t) = \int \sin(t^2) \ dt \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes i think this is a trap rule Q

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1or where \( F(t) = \sin(t^2) \), or what? What's your definition of F?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the first...the integral of

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Well, by the Fundamental Theorem of Calculus, the rate of change of F, is the derivative dF/dt is given by \[ dF/dt = \sin(t^2) \] Now integrals find averages of things. The average of a function \( f(t) \) over an interval [a,b] is given by \[ \frac{1}{ba} \int_a^b f(t) \ dt \] You're told that \[ \frac{1}{31} \int_1^3 \sin(t^2) \ dt = k \] Hence ...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Hence what must \[ \int_1^3 \sin(t^2) \ dt \] be equal to?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.01/2 of the approximation of the integral?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1No need to approximate, none at all.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0they ask for it in terms of k

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Yes ... read again the last equations I wrote up there for you.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok....thank you so much for walking me thru it
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