I don't know how to solve this with the absolute value.
Find the value of c: \[ \int_{0}^{c} |x(1-x)|dx=0 \]
Please, if possible, make a solution step-by-step. Thank you and sorry for the poor english.
2026-04-01 03:06:59.1775012819
Calculus Apostol, 1.26 exercise 21 b
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HINT:
If $c\le 1$, then $\frac{c^2}{2}-\frac{c^3}{3}=0$.
If $c>1$, then $\frac{1}{2}-\frac{1}{3}+\frac{c^3}{3}-\frac{c^2}{2}-\frac{1}{3}+\frac{1}{2}=0 \Rightarrow \frac{c^2}{2}-\frac{c^3}{3}=\frac{1}{3}$.
Now try it out.