Formula

Tags

• antiderivative
• integral definida
• integral definite FTC theorem fundamental of calculus
• property
• teorema fundamental

Explore the idea

Variables

• $x$Variable independiente (variable de integración)
• $t$Parámetro o variable auxiliar
• $a$Constante real (a menudo $a>0$)
• $f$Función integrando

Related formulas

• Related

  Formula

  $$f\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b) \Rightarrow \exists c\in(a,b): f'(c)=\frac{f(b)-f(a)}{b-a}$$
  Open formulaOpen in section

• Related

  Formula

  $$\int_a^b f(x)\,dx\le\int_a^b g(x)\,dx.$$
  Open formulaOpen in section

• Related

  Formula

  $$G'(x)=f(x).$$
  Open formulaOpen in section

• Related

  More generally, by the chain rule:

  $$\frac{d}{dx}\int_a^{g(x)}f(t)\,dt=f(g(x))g'(x).$$
  Open formulaOpen in section

• Related

  With both limits variable:

  $$\frac{d}{dx}\int_{u(x)}^{v(x)}f(t)\,dt =f(v(x))v'(x)-f(u(x))u'(x).$$
  Open formulaOpen in section

• Related

  Formula

  $$\int_a^b f(x)\,dx=F(b)-F(a).$$
  Open formulaOpen in section