Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(s) = s (t â t2)6dt 5

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04-05-2018
Mathematics

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Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(s) = s (t â t2)6dt 5

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LammettHash LammettHash · Answer 1 · 2018-05-04T18:30:14+02:00

LammettHash LammettHash

04-05-2018

Assuming it's

[tex]g(s)=\displaystyle\int_5^s(t-t^2)^6\,\mathrm dt[/tex]

By the FTC, we have

[tex]\dfrac{\mathrm dg}{\mathrm ds}=(s-s^2)^6\cdot\dfrac{\mathrm d}{\mathrm ds}s=(s-s^2)^6[/tex]

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