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

Question

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 · Answer

*Rewriting to use TeX*
$$\int\limits_{}^{}(85 - 3\sqrt(25-t))dt$$
equal to
$$2(25-t)^{3/2}+85t$$
and not
$$85t - 2(25-t)^{3/2}$$

Why?

mr.math · Answer

Use a substitution $u=25-t$ and see what you get.

phi · Answer

or take the derivative of each of your answers.  Only one will give the correct result.

mr.math · Answer

I see where you went wrong. You replaced $dt$ by $du$ and this is wrong, because $u=25-t \implies du=-dt$. Makes sense?

anonymous · Answer

How does u = (25-t) imply that du = -dt?

mr.math · Answer

If u=25-t, what's du/dt?

mr.math · Answer

The derivative of u with respect to t is obviously $\frac{du}{dt}=-1$. Multiply both sides by $dt$ you get $du=-dt$.