İntegral Hesap Makinesi
Bu integral hesap makinesi (polinomlar için) belirsiz ve belirli integralleri tam olarak bulur, her terim için kuvvet kuralını gösterir.
Sonuç
Değerleri girin ve sonucu görmek için Hesapla’ya dokunun.
Formül
The reverse power rule (for n ≠ −1).
The fundamental theorem of calculus.
Bu hesap makinesi nasıl kullanılır
- Type the polynomial and choose indefinite or definite.
- For a definite integral, enter the lower and upper limits.
Çözümlü örnekler
∫ 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.
Sık yapılan hatalar
- 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.
Sık sorulan sorular
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.