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anonymous
 4 years ago
Calculus question. Why is
∫85−3(√25−t)dt
equal to
2(25−t)3/2+85t
and not
85t−2(25−t)3/2
anonymous
 4 years ago
Calculus question. Why is ∫85−3(√25−t)dt equal to 2(25−t)3/2+85t and not 85t−2(25−t)3/2

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0*Rewriting to use TeX* \[\int\limits_{}^{}(85  3\sqrt(25t))dt\] equal to \[2(25t)^{3/2}+85t\] and not \[85t  2(25t)^{3/2}\] Why?

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1Use a substitution \(u=25t\) and see what you get.

phi
 4 years ago
Best ResponseYou've already chosen the best response.0or take the derivative of each of your answers. Only one will give the correct result.

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1I see where you went wrong. You replaced \(dt\) by \(du\) and this is wrong, because \(u=25t \implies du=dt\). Makes sense?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0How does u = (25t) imply that du = dt?

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1If u=25t, what's du/dt?

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1The derivative of u with respect to t is obviously \(\frac{du}{dt}=1\). Multiply both sides by \(dt\) you get \(du=dt\).
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