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

Riemann sum problem that I need solved! (The problem is attached as a screenshot)-example-1
User Quaternion
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1 Answer

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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.

User Sumon
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