Breakdown of the FTC
Before looking at any activities, let's look at each part of FTC part 1.
First, we have the integral from a to b. What do we want our starting and ending time to be? Since we are looking at the ladybug's path of movement, it will be easiest to begin when the ladybug is standing still. So let's start at a = 0 seconds. b can be any end time we want it to be. We could choose 10 seconds, 20 seconds, 1 minute, 2 minutes... the list goes on.
f'(x) represents the velocity of the ladybug. This tells us how fast the ladybug is crawling.
dx means we are integrating in respect to the variable x. In fact, this will also tell us what our "subintervals" are, but we will explore this in a little bit.
Now, onto the right side of the equation. After we integrate, we will be able to take f(x), the integrated function of f'(x), and plug in the starting and end times.
Why do you think this works? Does f(b) - f(a) really tell us the total distance covered?
Click here to explore the excel activity!
First, we have the integral from a to b. What do we want our starting and ending time to be? Since we are looking at the ladybug's path of movement, it will be easiest to begin when the ladybug is standing still. So let's start at a = 0 seconds. b can be any end time we want it to be. We could choose 10 seconds, 20 seconds, 1 minute, 2 minutes... the list goes on.
f'(x) represents the velocity of the ladybug. This tells us how fast the ladybug is crawling.
dx means we are integrating in respect to the variable x. In fact, this will also tell us what our "subintervals" are, but we will explore this in a little bit.
Now, onto the right side of the equation. After we integrate, we will be able to take f(x), the integrated function of f'(x), and plug in the starting and end times.
Why do you think this works? Does f(b) - f(a) really tell us the total distance covered?
Click here to explore the excel activity!