요금제

적분 계산기

이 적분 계산기(다항식용)는 부정적분(원시함수)과 정적분을 정확하게 구하고, 각 항의 거듭제곱 법칙을 보여 줍니다.

거듭제곱에는 ^를 쓰세요. 예: 4x^3 - x + 2

결과

값을 입력하고 계산을 누르면 결과가 표시됩니다.

공식

∫axn dx=an+1xn+1+C\int a x^n \, dx = \frac{a}{n + 1} x^{n+1} + C

The reverse power rule (for n ≠ −1).

∫abf(x) dx=F(b)−F(a)\int_a^b f(x)\,dx = F(b) - F(a)

The fundamental theorem of calculus.

이 계산기 사용법

  1. Type the polynomial and choose indefinite or definite.
  2. For a definite integral, enter the lower and upper limits.

풀이 예제

∫ from 0 to 2 of 3x² dx

An antiderivative of 3x² is x³.

F(2) − F(0) = 8 − 0 = 8.

Easy: an indefinite integral

Add 1 to each power and divide by the new power: x² → x³/3, and 4x → 4x²/2 = 2x².

∫(x² + 4x) dx = x³/3 + 2x² + C.

Hard: a definite integral with a negative limit

Antiderivative: F(x) = x³/3 − x² + 3x.

F(2) = 8/3 − 4 + 6 = 14/3 and F(−1) = −1/3 − 1 − 3 = −13/3.

∫ from −1 to 2 = F(2) − F(−1) = 14/3 + 13/3 = 27/3 = 9.

자주 하는 실수

  • Forgetting + C on an indefinite integral.
  • Subtracting the wrong way: a definite integral is F(upper) − F(lower).
  • Sign slips at a negative limit: F(−1) = −1/3 − 1 − 3, and subtracting it adds 13/3.

자주 묻는 질문

Can it do partial fraction integration?

Not directly — it integrates polynomials. For a fraction such as 1/((x − 1)(x + 2)), split it first with the Partial Fractions Calculator; each simple fraction then integrates to a logarithm.

What is + C?

Any constant differentiates to zero, so every antiderivative is defined up to a constant C.

Can it integrate sin x or eˣ?

This calculator handles polynomials. Sumzo AI can help with other functions.

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