Definite Integrals

A definite integral gives the signed area between a curve and the \(x\)-axis from \(x=a\) to \(x=b\).

\[\int_a^b f(x)\,dx=F(b)-F(a).\]

Properties

• \(\int_a^a f(x)\,dx=0\)
• \(\int_a^b f(x)\,dx=-\int_b^a f(x)\,dx\)
• \(\int_a^b f(x)\,dx+\int_b^c f(x)\,dx=\int_a^c f(x)\,dx\)