# Need help in calculus question?

a) Consider a body that starts moving from rest at time t = 0s with speed v(t) given by v(t) = (t2 + 5t)m/s. You are supposed to find the distance traveled by the body from time t = 0s until time t = 10s. (a) First, divide the time interval into five equal segments. Find the distance traveled in each segment approximately by multiplying the speed of the body at the midpoint of each segment by the time interval of the segment. Add these little distances to find the total distance traveled by the body.

The graph would be an upwards curve so like how do you divide that into segments to find the area?

b) The definite integral can be found by finding the antiderivative of v(t) and applying the fundamental theorem of calculus.

For part b are we just integrating the equation and substuiting 10 and 0 in it 🤕?

### 1 Answer

- alexLv 74 months ago
a/

v(t) = (t^2 + 5t)

2v(1)+2v(3)+2v(5)+2v(7)+2v(9) = ...

b/

integrate v(t)dt , from t=0 to t=10

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