AP Calculus: Applications of Integration flashcards

Question 1

What is the distance travelled along the path of a curve called?

Accepted Answer

Arc length

Question 2

What curve does a uniform-density cable take when it hangs between two supports?

Accepted Answer

A catenary, y = a cosh(x/a)

Question 3

What is the point where a system's whole mass could be placed without changing its moment?

Accepted Answer

Center of mass

Question 4

What is the geometric center of a region called?

Accepted Answer

Centroid

Question 5

What is the intersection of a plane with a solid object called?

Accepted Answer

A cross-section

Question 6

Which special case of the slicing method applies to a solid of revolution whose slices are disks?

Accepted Answer

The disk method

Question 7

Which special case of the slicing method applies to a solid of revolution whose slices are washers?

Accepted Answer

The washer method

Question 8

What is the time called that it takes an exponentially growing quantity to double?

Accepted Answer

Doubling time

Question 9

Systems following y = y0·e^(−kt) show which kind of behavior?

Accepted Answer

Exponential decay

Question 10

Systems following y = y0·e^(kt) show which kind of behavior?

Accepted Answer

Exponential growth

Question 11

What is the time called that it takes an exponentially decaying quantity to fall to half?

Accepted Answer

Half-life

Question 12

In terms of the rate k, what formula gives the half-life of an exponentially decaying quantity?

Accepted Answer

(ln 2)/k

Question 13

Which law says the force needed to stretch or compress a spring is proportional to its displacement from equilibrium?

Accepted Answer

Hooke's law

Question 14

What is the term for the pressure that water exerts on a submerged object?

Accepted Answer

Hydrostatic pressure

Question 15

What is a thin sheet of material called when it is treated as two-dimensional for mathematical purposes?

Accepted Answer

A lamina

Question 16

Which method finds a solid of revolution's volume by splitting it into nested cylindrical shells?

Accepted Answer

The method of cylindrical shells

Question 17

Compared with the disk and washer methods, the shell method integrates with respect to which variable?

Accepted Answer

The opposite variable

Question 18

What do you call a solid formed by revolving a plane region about a line in its plane?

Accepted Answer

A solid of revolution

Question 19

If a region is symmetric about a line, where does its centroid lie?

Accepted Answer

On that line (symmetry principle)

Question 20

What is the energy needed to move an object called, in physics?

Accepted Answer

Work

Question 21

When the force is constant, how is work expressed?

Accepted Answer

Force multiplied by distance

Question 22

What is the piece of a cone left after a plane parallel to its base cuts it called?

Accepted Answer

A frustum

AP Calculus: Applications of Integration flashcards

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