Introduction to FTC Part 1
We have learned about The Fundamental Theorem of Calculus since high school, but to completely comprehend what the equation is telling us and to conceptually grasp it is another matter. The way we can think about this visually is to imagine a ladybug sitting on a leaf without moving. Thus, the distance covered is 0 at the start time of a=0 seconds. As the ladybug begins crawling forward, the position or distance covered will increase by a certain amount depending on the ladybug's velocity. By knowing the velocity and multiplying this by the distance covered, broken into even segments otherwise known as delta x or subintervals, we can find the total distance the ladybug travels from time a=0 seconds to some time b seconds!
But how is this possible? By splitting up the entire time interval into even segments, we can add up individual distances that the ladybug travels and add them up one by one. (We will explore this later!)
Why do we want to know this? We are using a simple scenario of a ladybug crawling along a leaf. However, what if we wanted to know how many miles we've driven in a car at 60 mph after sixty minutes has passed? What if we are riding a rollercoaster and want to know how far it's traveled after forty-five seconds? The answer to these questions is easier than you might think. But how can we intuitively come up with an answer to these them? This theorem provides us with the necessary tools.
Click here to look at a breakdown of the formula!
But how is this possible? By splitting up the entire time interval into even segments, we can add up individual distances that the ladybug travels and add them up one by one. (We will explore this later!)
Why do we want to know this? We are using a simple scenario of a ladybug crawling along a leaf. However, what if we wanted to know how many miles we've driven in a car at 60 mph after sixty minutes has passed? What if we are riding a rollercoaster and want to know how far it's traveled after forty-five seconds? The answer to these questions is easier than you might think. But how can we intuitively come up with an answer to these them? This theorem provides us with the necessary tools.
Click here to look at a breakdown of the formula!