Calculate Total Data Downloaded Using Speed Function

Published on May 25, 2026

Calculus

Learn how to find the total amount of data downloaded by integrating the given speed function S(t) = 50 - 2t over a time interval of 10 seconds.

Question

Answer

To find the total amount of data downloaded, we need to integrate the download speed function

over the given time interval.

1. Identify the given information:

The download speed function is .
The time interval is from to seconds.

2. Set up the integral:
The total amount of data

is the integral of the speed function with respect to time:

3. Evaluate the integral:
Find the antiderivative of

Now, apply the limits of integration from

Final Answer:
The total amount of data downloaded in 10 seconds is 400 units of data.

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