The following rules require all relevant integrals to exist. _aaf(x), dx=0 _abf(x), dx=- _baf(x), dx _acf(x), dx= _abf(x), dx+ _bcf(x), dx Reversing the limits reverses the subtraction: F(a)-F(b)=-[F(b)-F(a)]. When the interval is split at b, the two contributions add because [F(b)-F(a)]+[F(c)-F(b)]=F(c)-F(a). Constant multiples and sums can be integrated term by term. Check undefined or unbounded points before applying these rules.

The following rules require all relevant integrals to exist.

\(\int_a^af(x)\,\mathrm dx=0\qquad\int_a^bf(x)\,\mathrm dx=-\int_b^af(x)\,\mathrm dx\)

\(\int_a^cf(x)\,\mathrm dx=\int_a^bf(x)\,\mathrm dx+\int_b^cf(x)\,\mathrm dx\)

Reversing the limits reverses the subtraction: \(\mathrm{F}(a)-\mathrm{F}(b)=-[\mathrm{F}(b)-\mathrm{F}(a)]\).

When the interval is split at \(b\), the two contributions add because \([\mathrm{F}(b)-\mathrm{F}(a)]+[\mathrm{F}(c)-\mathrm{F}(b)]=\mathrm{F}(c)-\mathrm{F}(a)\).

Constant multiples and sums can be integrated term by term. Check undefined or unbounded points before applying these rules.

Properties and Interpretation of Definite Integrals

Properties and Interpretation of Definite Integrals

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