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`.