{"uid":"cap__gFNP1qLZZSedl2KlwGzm","slug":"numora-calculus-integral-computation-c0e88274","name":"Numora Calculus Integral Computation","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numomo.vercel.app/api/calculus/integral","method":"POST","headers":{},"bodySchema":{"type":"object","required":["a","b","fn"],"properties":{"a":{"type":"number"},"b":{"type":"number"},"fn":{"type":"string"},"method":{"type":"string"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_9FW881yCHxUKuIO1VfnTU","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Numerically integrates a mathematical function over a specified interval [a, b] and returns the computed result","exampleAgentPrompt":"Can you compute the definite integral of sin(x) from 0 to 3.14159 using the Numora math API?","exampleUseCases":[{"title":"Area under physics curve","prompt":"Calculate the definite integral of x^2 + 3*x from a=0 to b=10 — I need the exact numeric result for an engineering report."},{"title":"Financial probability integration","prompt":"Integrate the function exp(-x^2) from 0 to 2 so I can estimate a probability density for my statistics model."},{"title":"Signal energy calculation","prompt":"I need to find the energy of a signal — compute the integral of sin(x)^2 from 0 to 6.2832 (that's 0 to 2π) using the trapezoidal method."}],"resultDescription":"Returns a JSON object with a boolean 'success' field, a 'result' object containing the numeric value of the definite integral, and a 'computation' string describing in plain English what was computed (e.g. 'Definite integral of sin(x) from 0 to 3.14159').","failureModes":["Invalid or unparseable function expression in 'fn' — returns error with parse failure message","Bounds a and b not provided or non-numeric — returns validation error","Division by zero or singularity within the integration interval — may return NaN or error","Unsupported integration method string — may fall back to default or return error","Network/server timeout on complex functions requiring many evaluations"],"whenToPreferThis":"Choose this endpoint when you need a reliable, serverless numerical integration of a mathematical function over a closed interval without setting up a local math library. Ideal for AI agents needing on-demand calculus inside workflows, especially when the function is expressible as a string formula and exact symbolic integration is not required. Prefer this over symbolic CAS tools when you only need the numeric result and want zero infrastructure overhead.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:56:55.982Z","isFirstParty":false}