## 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

1. anonymous

*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?

2. Mr.Math

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

3. phi

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

4. Mr.Math

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

5. anonymous

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

6. Mr.Math

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

7. Mr.Math

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