When Calculus Becomes Our Love Language

Nano

The integral of x² is simple - add one to the exponent and divide by the new exponent.

Nano

Therefore, ∫x²dx = x³/3 + C.

Hakari

But why does adding one to the exponent work? My brain doesn't understand the love between x and 3!

Karane

Baka Hakari! It's just a formula - stop overthinking it with your wedding brain!

Karane

(Though... I don't really get why either...)

Nano

Observe! I'll prove it using the area under the curve!

Nano

As these rectangles get infinitely thin, their sum approaches exactly x³/3.

Shizuka

(She's using Riemann sums... but why does the area formula give the antiderivative?)

Hakari

I got it! Integration is like planning a wedding - you collect all the small moments to create something beautiful!

Nano

(Her analogy... it's mathematically nonsensical, yet... somehow it works?)

Karane

That's... that's not how math works at all, Hakari...

Karane

(But if it helps her understand, maybe love really is the ultimate integral...)