Integrals and Costumes

A few days later, we were in the middle of our applied mathematics class. Professor Anderson, a tall and thin man with round glasses that always matched his overly formal tie, was giving a lecture on how integrals could be used in medicine to model the diffusion of drugs in the human body. His voice echoed through the classroom as he wrote equations on the board with surgical precision.

—Integration allows us to calculate not only the area under a curve but also dynamic processes like the elimination of a drug from the bloodstream —he explained, pointing to a graph showing a descending curve—. Imagine you have a patient who has been administered medication. The rate of elimination depends on factors such as the current concentration of the drug in the body and the patient's kidney function. Using a definite integral, we can determine how long it will take for the drug to reach safe levels or even be completely eliminated.

All the students were attentive, taking notes on their iPads or laptops. Even Olivia, who usually preferred drawing caricatures of professors rather than paying attention, seemed unusually focused. She had her eyes glued to her iPad screen, typing quickly and occasionally nodding to herself whenever the professor mentioned something important.

Lindsay, sitting next to me, noticed this too and leaned toward her.

—Since when are you so interested in applied math? —she whispered, incredulous—. I didn't know you had this hidden side.

Olivia looked up from her iPad for a moment and smiled innocently.

—Oh, of course I understand all this —she responded, pretending confidence—. It's fascinating how integrals can help save lives, isn't it?

—Understand it? —Lindsay raised an eyebrow, looking at her skeptically—. Really?

—Well… maybe not everything —Olivia admitted, lowering her voice—. But I want to seem like I do. Besides, if I take good notes, I can convince someone else to explain it to me later.

Lindsay let out a soft laugh but quickly refocused on her own iPad, where she already had several pages filled with graphs and detailed annotations. It was impressive how she could stay so focused throughout the entire class.

For my part, I was also taking notes, though not necessarily because it was hard to follow the topic. I just preferred having an organized record of what the professor was explaining. Plus, it was a good excuse to avoid participating when he threw questions into the air.

—Now, imagine you're trying to calculate the total amount of a drug that has been absorbed by the body over a specific period of time —Professor Anderson continued, adjusting his glasses—. How would you apply a definite integral in this case?

Olivia stopped typing for a second and leaned toward me.

—Sack, you're good at this. What would you do? —she asked in a whisper.

—I'd use the absorption rate equation and integrate it with respect to time —I replied without looking away from my iPad—. That way, we'd get the area under the curve, which represents the total amount absorbed.

—Of course, obvious —Olivia said, nodding as if she'd understood perfectly—. That's exactly what I was going to say.

I rolled my eyes but didn't say anything. I knew Olivia had no idea what she was talking about, but her effort to appear interested was almost admirable.

The professor continued with his explanation, and just when we thought the class would end without incident, he decided to ask a direct question.

—Miss Hart —he said, looking at Olivia—, based on what we've just discussed, how would you use a definite integral to calculate the total amount of a drug that has been absorbed by the body over a specific period of time?

The entire class fell silent. All eyes turned to Olivia. It was well known among the students that Olivia didn't usually excel in technical classes, and many expected her to mumble some vague answer or simply admit she didn't know.

But to everyone's surprise, Olivia looked up from her iPad with a confident (or at least feigned) expression and answered:

—I'd use the absorption rate equation and integrate it with respect to time. That way, we'd get the area under the curve, which represents the total amount absorbed.

There was a moment of absolute silence in the room. Then, some students began murmuring among themselves, clearly surprised. Lindsay looked at me with wide eyes, and I had to suppress a smile. It was obvious that Olivia had repeated word-for-word what I had just told her a few minutes earlier.

Professor Anderson blinked a couple of times, visibly impressed.

—Excellent answer, Miss Hart —he finally said, nodding in approval—. I see you've been paying close attention.

Olivia smiled broadly, as if she had just won a Nobel Prize.

—Thank you, Professor —she responded, feigning modesty—. I'm just trying to keep up.

When the professor turned back to the board, Lindsay leaned toward Olivia.

—Seriously? —she whispered, a mix of amazement and amusement in her voice—. Was that all thanks to Sack?

—I have no idea what you're talking about —Olivia replied, still smiling—. I'm full of surprises.

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After class, we walked together to the cafeteria. Olivia kept chattering about her ideas for Halloween, but soon Lindsay changed the subject.

—By the way, don't forget we need to submit our biology project soon —she said, checking her calendar on her iPad—. We need to meet up soon to finish the final details.

—The genetics lab project? —I asked, recalling the long hours we'd spent working on it.

—Exactly —Lindsay replied—. I think we just need to analyze the final data and write the conclusion. If we organize well, we can finish it in a couple of sessions.

—Great —Olivia said, feigning enthusiasm—. Nothing like spending hours locked in a lab to celebrate university life.

—It's necessary —Lindsay responded, smiling—. Besides, if we do it well, it could improve our final grades.

—Alright, alright —Olivia said, raising her hands in surrender—. I promise not to complain too much. But only if you let me listen to music while I work.

—Deal —Lindsay said, laughing.

We fell silent for a moment as we walked, enjoying the fresh air of the campus. Despite everything, there was something comforting about our everyday conversations and how, even amidst technical topics like integrals or pending projects, we always found ways to laugh.

Maybe Lindsay was right. Maybe Halloween wouldn't be so bad. And maybe, just maybe, it would be worth trying.

The weekend arrived faster than expected, and the three of us spent practically the entire Saturday locked in the lab working on the genetics project. There were moments of frustration, especially when the data didn't match our hypotheses, but there were also laughs when Olivia tried to distract us with her impressions of the professors.

Finally, by late afternoon, we managed to finish the analysis and write the conclusion. Exhausted but satisfied, we decided to take a break and enjoy the evening by doing something fun.

—How about we go to the movies? —Olivia suggested, stretching in her chair—. Ever since I saw the trailer for that sci-fi movie, I've wanted to watch it.

—Sounds good to me —Lindsay said, closing her laptop—. We deserve it after all this work.

I nodded, though I wasn't particularly fond of movie theaters. But something about Olivia's excitement and Lindsay's tired smile made me accept without hesitation.

We went to the cinema at the mall near campus. The movie was thrilling, full of unexpected twists and impressive visual effects. During the screening, I noticed how Lindsay slowly curled up against me, seeking warmth or perhaps just relaxing after the long day. Without thinking too much, I put my arm around her shoulders, pulling her a little closer. She didn't say anything, but I felt her relax even more against me.

Olivia, sitting on the other side of Lindsay, gave us a quick glance and smiled to herself, but didn't make any comments. Instead, she focused on the screen, though occasionally she muttered some sarcastic remark about the plot.

As we left the theater, the cool night air greeted us. Olivia yawned dramatically as we walked back to campus.

—That was exactly what I needed —she said, smiling—. Now, all that's left is surviving Halloween and final exams.

—One at a time —Lindsay replied, laughing.