Question

Why is: (posting question in a reply)...

Answer 1

\[\int\limits_{}^{}85-3\sqrt(25-t)dt\] equal to
\[2(25-t)^{3/2} + 85t \]
and not
\[85t - 2(25-t)^{3/2}\]

Answer 2

u-substitution\[u=25-t\]\[du=-dt\to dt=-du\]so our integral becomes\[\int\limits_{}^{}3\sqrt(25-t)dt=-3\int\sqrt udu=-2u^{3/2}=-2(25-t)^{3/2}\]so as you can see, the u-sub caused the sign on the coefficient to change