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Basic Properties of Definite Integrals

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What are five basic properties of definite integrals?
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$\int_{a}^{a} f (x) d x = 0$ $int_a^a f(x) dx=0$

$\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x$ $int_a^b f(x) dx=-int_b^a f(x) dx$

$\int_{a}^{b} [f (x) + g (x)] d x = \int_{a}^{b} f (x) d x + \int_{a}^{b} g (x) d x$ $int_a^b [f(x)+g(x)]dx=int_a^b f(x) dx+int_a^b g(x) dx$

$\int_{a}^{b} k f (x) d x = k \int_{a}^{b} f (x) d x$ $int_a^b k f(x)dx=k int_a^b f(x) dx$

$\int_{a}^{b} f (x) d x = \int_{a}^{c} f (x) d x + \int_{c}^{b} f (x) d x$ $int_a^b f(x) dx=int_a^c f(x) dx + int_c^b f(x) dx$

I hope that this was helpful.
Wataru · 4 · Oct 3 2014

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Introduction to Integration

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