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A definite integral computes the net signed area between a function f(x) and the x-axis over an interval [a, b]. It is one of the two fundamental operations of calculus (the other being differentiation) and is the basis for computing areas, volumes, arc lengths, work, probability, and much more. The Fundamental Theorem of Calculus connects integrals to antiderivatives.

단계별 가이드

1Definite integral ∫[a,b] f(x) dx = F(b) − F(a) where F is the antiderivative of f
2Our calculator uses Simpson's Rule with 1000 intervals for high-precision numerical approximation
3Simpson's Rule: ∫ ≈ (h/3)[f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + f(xₙ)]
4Error decreases as O(h⁴) — much faster than the Trapezoidal Rule's O(h²)
5Supported functions: x^n, sin, cos, tan, sqrt, ln, exp, pi, e

풀어진 예시

입력

∫[0,1] x² dx

결과

1/3 ≈ 0.3333

Antiderivative of x² is x³/3; F(1)−F(0) = 1/3

입력

∫[0,π] sin(x) dx

결과

2.0000

Antiderivative of sin(x) is −cos(x); −cos(π)+cos(0) = 2

입력

∫[1,e] ln(x) dx

결과

1.0000

Integration by parts gives [x·ln(x)−x] from 1 to e = 1

자주 묻는 질문

What is Integral Calc?

How accurate is the Integral Calc calculator?

The calculator uses the standard published formula for integral calc. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Integral Calc calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Integral Calc calculator use?

The core formula is: Definite integral ∫[a,b] f(x) dx = F(b) − F(a) where F is the antiderivative of f. Each step in the calculation is shown so you can verify the result manually.

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