Page 174 - Calculus Workbook For Dummies

In this part . . .

ntegration, like differentiation, is a highfalutin calculus
Iword for a simple idea: addition. Every integration
problem involves addition in one way or another. What
makes integration such a powerful tool is that it sort of
cuts up something (the weight of a large dome, the length
of a power cable, the pressure on the walls of a pipe, and
so on) into infinitely small chunks and then adds up the
infinite number of chunks to arrive at a precise total.
Without integration, many such problems can only be
approximated. Part IV gives you practice with integration
basics, techniques for finding integrals, and problem solv-
ing with integration.

Infinite series is a topic full of bizarre, counter-intuitive
results that have fascinated thinkers for over 2,000 years.
Zeno of Elea (5th century B.C.) gave us his famous para-
dox about the race between Achilles and the tortoise (the
resolution of the paradox involves limits — see Calculus
For Dummies). Your task with infinite series problems is
to decide whether the sum of an infinitely long list of num-
bers diverges (adds up to infinity — usually) or converges
(adds up to an ordinary, finite number).