#86 · Calculus · The definite integral

The area under a parabola

Long before calculus, this area was known. Show, using a limit of rectangles, that the region under $y = x^{2}$ from $x = 0$ to $x = 1$ has area exactly $\frac{1}{3}$ .

~14 minWritten answer · check your work with LemmaRiemann sumsSum of squares

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.