## Integration

The integral of a function f defines a new function, which may have the interpre-

tation of an area or as the “reverse” of differentiation. For example, the computa-

tion of consumer surplus and dead-weight loss involve the calculation of area.

Given a demand function P(Q) and market price p, the consumer surplus is

defined as the area under the demand curve above price and is used as a mea-

sure of the welfare generated by the existence of that market. The technique of

integration provides a means of determining this area. In a second type of prob-

lem, it is useful to identify a function as the derivative of another function. For

example, the rate of return on an asset – the change in the value of the asset per

unit of time – may be viewed as the derivative of the value of the asset. Thus,

knowing the derivative of the value of the asset with respect to time, say v′(t), it

is necessary to determine the value of the asset, v(t), from this derivative – given

v′(t), v(t) must be found. These problems are solved by integration.