Belirli ve Belirsiz İntegral Formülleri

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Belirli ve Belirsiz integralin özellikleri, formülleri. Belirli ve belirsiz integral formül listesi.

BELİRLİ İNTEGRAL

f:[a,b]→R sürekli bir fonksiyon ve ∀x∈[a,b] için,

F ‘ (x)= f(x)  ise

\displaystyle \int_{b}^{a}{f\left( x \right)}dx=F\left( x \right)\left| _{a}^{b} \right.=F\left( b \right)-F\left( a \right)

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BELİRLİ İNTEGRAL FORMÜLLERİ

f ve g:[a,b]→R sürekli iki fonksiyon var ve c∈(a,b), k ∈ R için,

\displaystyle *\int_{a}^{a}{f\left( x \right)}dx=0

\displaystyle *\int_{a}^{b}{f\left( x \right)}dx=-\int_{b}^{a}{f\left( x \right)}dx

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\displaystyle \begin{array}{l}*\int_{a}^{b}{f\left( x \right)}dx=\int_{a}^{c}{f\left( x \right)}+\int_{c}^{b}{f\left( x \right)}dx\\(c\in \left( a,b \right))\end{array}

\displaystyle *\int_{a}^{b}{\left[ f\left( x \right)\mp g\left( x \right) \right]}dx=\int_{a}^{b}{f\left( x \right)}dx\mp \int_{a}^{b}{g\left( x \right)}dx

\displaystyle *\int_{a}^{b}{k.f\left( x \right)}dx=k.\int_{a}^{b}{f\left( x \right)}dx

BELİRSİZ İNTEGRAL FORMÜLLERİ

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\displaystyle *\int{f'\left( x \right)}dx=F\left( x \right)+C

\displaystyle \begin{array}{l}*\int{\alpha f\left( x \right)}dx=\alpha \int{f\left( x \right)}dx\\\left( \alpha \in R \right)\end{array}

\displaystyle *\int{\left[ f\left( x \right)\mp g\left( x \right) \right]}dx=\int{f\left( x \right)}dx\mp \int{g\left( x \right)}dx

\displaystyle *\int{d\left[ f\left( x \right) \right]}=f\left( x \right)+C

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\displaystyle *\frac{d}{dx}\left[ \int{f\left( x \right)}dx \right]=f\left( x \right)

\displaystyle *d\left[ \int{f\left( x \right)}dx \right]=f\left( x \right)dx


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