Integration by Parts - it's all just counting!

https://annasmathpage.com Note, I should have said the area of the integral we are looking for is "the side piece" or "the area to the left of the function's curve" rather than the area above the function's curve. That wording "the area above the function's curve" worked for the problem in my last video but is not quite accurate for the problem in this video. We could also just refer to it as "the mystery piece" the piece we are trying to find the area of. Can you master the Integration by Parts formula just by counting? Yes, you can. In this video, I break down the confusing textbook formula and strip Integration by Parts down to its concrete core. What you’ll learn: ∫udv = uv - ∫vdu is actually just a simple subtraction puzzle. We can turn our rectangles sideways to count them. When we do this, we aren't counting vertical rectangles anymore, we are counting horizontal rectangles that stack up the wall from y=2 to y=6. Their width is x, and they stretch all the way from the blue line x=0 (the y-axis) out to our diagonal function line f(x). This is an ultimate "ah ha" moment. Pure Concrete Calculus: Watch me trace the function line directly onto the blocks and prove the calculus formula matches the concrete model. No matter how advanced math gets, remember: Math is the study of numbers All we do with numbers is count We build rectangles to facilitate counting When it's no fun get back to one If this visual breakthrough made Integration by Parts finally "click" for you, hit that Subscribe button and leave a comment below letting me know what calculus concept we should build next.