Penjelajah Jumlah Riemann

Lihat bagaimana persegi panjang kiri/kanan, trapesium, titik tengah, dan busur Simpson mendekati ∫ f(x) dx. Pantau plot, periksa langkah kerja, bandingkan dengan referensi Simpson adaptif, ekspor CSV, dan salin tautan berbagi.

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Ketik ekspresi analitik seperti sin(x), exp(-x^2), x^3 - 2x, atau gabungkan fungsi ln, abs, sgn, dan konstanta seperti pi.

Perlu demo cepat di kelas? Nyalakan opsi isi untuk menonjolkan luas bertanda, bandingkan konvergensi tiap aturan saat n membesar, lalu pakai tombol CSV atau LaTeX untuk membuat lembar kerja seketika.

Input & opsi

Visualisasi

f(x) Approximation Simpson segments

Result

Rule applied
Approx Sₙ
Reference integral
Absolute error
Relative error

How it's calculated

    FAQ

    Which Riemann sum rule should I pick?

    Left/right sums follow the orientation of rectangles, which is great for quick estimates but can over- or undershoot when f is monotone. The trapezoid rule is second-order accurate and balances speed with precision. Simpson's rule reaches fourth-order accuracy on smooth functions, while midpoint splits the difference with a symmetric single-rectangle view.

    Why must Simpson's rule use an even n?

    Simpson's rule joins point triplets with quadratics, so the interval must break into an even number of subintervals. The explorer automatically increases n by 1 when needed and highlights the adjustment in the steps.

    How many subintervals n should I use?

    For smooth functions start with n = 50–100 and increase n to reduce error. Simpson converges faster but requires even n; the tool adjusts n automatically when needed.

    Can I enter piecewise or non‑analytic functions?

    Yes. You can use abs, sgn, and constants like pi. Non‑finite evaluations are skipped and treated as zero; the step log notes any skipped points.