Mr. Integral
Math notes/Calculus I/The Integral

Net Change, Distance and a Calculus I Checkpoint — Cheat sheet

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Core rule

q(b)=q(a)+∫abq′(t)dt.q(b)=q(a)+\int_a^bq'(t)dt.

Displacement integrates velocity; distance integrates its absolute value. Average rate is net change divided by elapsed time.

Watch for

Split at velocity sign changes, include the initial amount, preserve units and respect physical domain constraints.