Question

Evaluate the definite integral

Answer 1

`\displaystyle\int_(x=9)^(x=10)x√(x-9)\,\mathrm dx`

Let
`y=x-9`, so that
`x=y+9` and
`\mathrm dx=\mathrm dy`. The integral is then equivalent to


`\displaystyle\int_(y=0)^(y=1)(y+9)\sqrt y\,\mathrm dy=\int_0^1(y^(3/2)+9y^(1/2))\,\mathrm dy=\frac{32}5`