Why do we use Integrals in Physics?

In my physics guide, I break down why we use integrals in physics to represent net change.

An object that’s subject to a constant force over time will accelerate at a constant rate. Therefore, its velocity v(t) is changing over time. Normally, we could calculate the distance Δs that the object traveled at a constant velocity through the equation: Δs=vt, but if the velocity is changing over time, we can’t use this equation.

Instead, we must take an integral which involves calculating the distance the object traveled ds throughout a small window in time dt through the equation: ds=v(t)*dt. We add up all of those small distances ds between two points in time through an integral to calculate the net distance traveled.

You can check out the full guide here which includes an entire section on calculus and its applications in physics.

I’ve also released a Bundle, priced at a 20% discount, which combines the Physics Guide and the ‘Algebra for STEM’ guide into ONE product by compressing all of the relevant algebra used in physics—ranging from prealgebra through precalculus—into one product with physics! Make sure to purchase the complete bundle to master the foundations of physics!

Down below, you can read about each product separately!

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The hardest part about math isn’t the raw calculations: it’s understanding what the math means when rearranging and graphing functions. Most students aren’t trained to interpret the math from a qualitative perspective which is why many students who are ‘good at math’ struggle in introductory chemistry, physics, and engineering courses.

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