Properties of the Definite Integral
Read this section to learn about properties of definite integrals and how functions can be defined using definite integrals. Work through practice problems 1-5.
Properties of the Definite Integral
As you read each statement about definite integrals, examine the associated Figure and interpret the property as a statement about areas.
Justification of Property 3: Using area: If then
represents the area of the rectangle with
and
, so
Using Riemann Sums: For every partition of the interval [a, b], and every choice of
, the Riemann sum is
so the limit of the Riemann sums, as the mesh approaches zero, is .
Justification of Property 4:
Property 5 can be justified using Riemann sums, but Fig. 2 graphically illustrates why it is true.