Question

Titiknya 10 dan 8 ∫x-8)( x-9) (x-10) dx

Answer 1

$\displaystyle\int_8^{10}(x-8)(x-9)(x-10)\,\mathrm dx$

Consider the substitution,

$y=x-9\implies\begin{cases}y-1=x-10\\y+1=x-8\\\mathrm dy=\mathrm dx\end{cases}$

so that the integral is equivalent to

$\displaystyle\int_{-1}^1y(y+1)(y-1)\,\mathrm dy$

Notice that

$f(y)=y(y+1)(y-1)\implies f(-y)=-y(-y+1)(-y-1)=-y(y-1)(y+1)=-f(y)$

which means $f(y)$ is odd, so

$\implies\displaystyle\int_{-1}^1f(y)\,\mathrm dy=0$

Perhaps more work than necessary, but it does make it easier to see that the original integrand exhibits some symmetry about $x=9$.