query in riemann sum approximation

Question

the velocity of a projectile fired straight into air is given by f(t)=160-9.8t m/sec, we have to calculate how far the projectile rises during the first 3 seconds by reimann sum approximation.

we calculate/approximate it by taking the lower and upper sum(i.e left and right end points).

we take three subintervals each of length 1, when we consider calculating by taking left end point the 3rd second misses out, and when we calculate by taking right end point the 0th second isnt included.

since we have to calculate first three seconds, but here we are calculating distance over 2 secs only, i.e 0-1 gives 1 sec and 1-2 gives 2nd second.

similarly 1-2 gives 1st sec and 2- 3 gives 2nd second,thereby giving us 2 secs.

so how come we are calculating for first three seconds??

is it that when intervals are increased we are able to calculate/approximate the distance from 0-3 seconds.

plz explain,would be great help.thank you

Answer 1

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