Home/Calculus II/Properties/Formula3.2. PropertiesFormulaIn 3.2. PropertiesFormulaCopy LaTeX∫aaf(x) dx=0\int_a^a f(x)\,dx=0∫aaf(x)dx=0Tagsantiderivativeintegral definidaintegral definite FTC propertiespropertyteorema fundamentalVariablesxxxVariable independiente (variable de integración)aaaConstante real (a menudo a>0a>0a>0)fffFunción integrandodxdxdxDiferencial respecto de xxxFound an error? Contact us.Related formulasRelatedFor a uniform partition, Δx=(b−a)/n\Delta x=(b-a)/nΔx=(b−a)/n:∫abf(x) dx=limn→∞∑i=1nf(xi∗)Δx.\int_a^b f(x)\,dx =\lim_{n\to\infty}\sum_{i=1}^{n}f(x_i^*)\Delta x.∫abf(x)dx=n→∞limi=1∑nf(xi∗)Δx.Open formulaOpen in sectionRelatedFormula∫abf(x) dx=−∫baf(x) dx\int_a^b f(x)\,dx=-\int_b^a f(x)\,dx∫abf(x)dx=−∫baf(x)dxOpen formulaOpen in sectionRelatedFormula∫abf(x) dx+∫bcf(x) dx=∫acf(x) dx\int_a^b f(x)\,dx+\int_b^c f(x)\,dx=\int_a^c f(x)\,dx∫abf(x)dx+∫bcf(x)dx=∫acf(x)dxOpen formulaOpen in sectionRelatedFormula∫ab[αf(x)+βg(x)] dx=α∫abf(x) dx+β∫abg(x) dx\int_a^b [\alpha f(x)+\beta g(x)]\,dx =\alpha\int_a^b f(x)\,dx+\beta\int_a^b g(x)\,dx∫ab[αf(x)+βg(x)]dx=α∫abf(x)dx+β∫abg(x)dxOpen formulaOpen in sectionRelatedFormula∫abf(x) dx≥0.\int_a^b f(x)\,dx\ge0.∫abf(x)dx≥0.Open formulaOpen in sectionRelatedFormula∫abf(x) dx≤∫abg(x) dx.\int_a^b f(x)\,dx\le\int_a^b g(x)\,dx.∫abf(x)dx≤∫abg(x)dx.Open formulaOpen in section