Question

Riemann sum problem that I need solved! (The problem is attached as a screenshot)

Answer 1

You need to find the exact distance, so a Riemann sum isn't exactly needed but can be used.

The sum-free way to do this is to integrate
`f(t)` over
`0\le t\le10`, assuming a starting position of
`p_0`.

`p_0+\displaystyle\int_0^(10)f(t)\,\mathrm dt`

`\implies p_0+\displaystyle3\int_0^(10)t\,\mathrm dt`

`\implies p_0+\frac{3t^2}2\bigg|0^(10)`

`\implies p_0+150`

The question says to use a graph (which isn't given), but the idea would have been to find the area under the curve
`f(t)=3t`, which would be a triangle whose area would be easy to find.