By 1:00 AM, he had finished the entire set. He leaned back, his eyes dry, his soul bruised, but victorious. He clicked back to the main menu of Paul’s notes and saw the full horror of the semester laid bare: Applications of Integrals, Parametric Equations, Polar Coordinates, Sequences and Series.
Paul taught him the Shell Method when the Washer Method made him want to smash his laptop. Paul demystified Integration by Parts with the simple mnemonic “LIATE.” And when the final exam loomed, Leo printed out Paul’s “Calculus II Cheat Sheet” and taped it to his wall like a sacred scroll. paul's online math notes calculus ii
Leo laughed. It was a hollow, tired laugh, but it was real. He bookmarked the page. By 1:00 AM, he had finished the entire set
He smiled. He could hear Paul’s voice in his head: “Alright, let’s work an example. This is a classic integration by parts problem. You’re going to let u = x^3 and dv = sin(x) dx. It’s going to take three passes, but you’ve got this.” Paul taught him the Shell Method when the