Integral Calculator
Symbolic antiderivatives + numeric definite integrals
f(x)
Symbolic: x^n, sin(x), cos(x), tan(x), e^x, 1/x
Numeric (Simpson): any expression with x — sin cos tan sqrt ln exp log ^
∫ f(x) dx =
∫ f(x) dx ≈
ErrorIntegral Calculator — Complete Guide & Instructions
MakeCard Integral Calculator solves calculus integrals two ways: symbolically for exact antiderivatives of polynomials, trig functions, e^x and 1/x, and numerically with Simpson's rule for definite integrals of almost any expression in x. It is aimed at Class 11–12 and engineering students checking homework, and anyone needing a quick area-under-the-curve value without installing math software.
How to Use Integral Calculator
- 1 Choose “Indefinite ∫” for a symbolic antiderivative or “Definite ∫ᵃᵇ” for a bounded numeric answer.
- 2 Type the function into the f(x) box — e.g. 3x^2 + 2x, sin(x), e^x or 1/x.
- 3 For definite mode, enter the Lower bound a and Upper bound b.
- 4 Click “Integrate”.
- 5 Read the result: “∫ f(x) dx = …” for symbolic answers or “∫ₐᵇ f(x) dx ≈ …” for the numeric value.
Key Features & Capabilities
- True symbolic antiderivatives — power rule, sin, cos, tan, e^x and 1/x are integrated exactly.
- Definite mode uses Simpson's rule for accurate numeric integration of arbitrary expressions.
- Accepts a wide numeric syntax: sin cos tan sqrt ln exp log and the ^ power operator.
- Clear result formatting — exact antiderivative or approximate definite value with bounds shown.
- Inline error messages that point at malformed expressions.
Supported Formats & Specifications
| Parameter | Specification |
|---|---|
| Symbolic Support | x^n polynomials, sin(x), cos(x), tan(x), e^x, 1/x |
| Definite Method | Simpson's rule numeric quadrature — any valid expression in x |
| Input Syntax | sin cos tan sqrt ln exp log ^ and standard arithmetic |
| Output | Exact antiderivative (indefinite) or decimal value (definite) |
| Processing | Entirely client-side, instant results |
Practical Everyday Use Cases
- Verifying antiderivatives while solving NCERT Class 12 integration exercises.
- Computing the area under a curve between two limits for physics or economics problems.
- Checking definite integrals in engineering mathematics assignments.
- Getting quick numeric integrals of functions with no elementary antiderivative.
- Cross-checking hand-done integration by parts results.
Pro Tips for Best Results
- Write powers with ^ — enter x^3, not x3; multiplication must be explicit: 2*x, not 2x.
- Use the symbolic Indefinite mode when you need the formula itself; switch to Definite for a number.
- For definite integrals of discontinous functions, split the range at the discontinuity and add the parts.
- sin(x) uses radians — convert degree problems to radians first.
Common Problems & Solutions
Check the supported syntax — use ^ for powers, * for multiplication, and write functions as sin(x), ln(x), e^x. Implicit multiplication like 2x is not parsed.
Definite mode returns an approximation. For oscillating or sharply curved functions the Simpson estimate can drift — narrow the interval or verify against the symbolic form.
Functions like 1/x blow up at x = 0 — make sure neither bound nor the interval crosses a singularity.
Privacy & Security
100% Client-Side Execution
All symbolic and numeric computation runs in your browser — expressions you enter are never sent to a server or stored.
Frequently Asked Questions
Everything you need to know about using Integral Calculator
An indefinite integral finds the antiderivative family (∫f(x)dx = F(x) + C); a definite integral evaluates the net area between two bounds and returns a number.
Type x^2 into the f(x) box in Indefinite mode and press Integrate — the tool returns x^3/3 + C instantly.
Simpson's rule — a numeric technique that fits parabolas over small subintervals; it is far more accurate than basic trapezoid or rectangle methods.
Yes — sin(x), cos(x), tan(x), e^x, ln-based forms and 1/x are supported in both modes.
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