Indefinite Integrals Exercises

Answer

 converges to 0.

Answer

 diverges.

Answer

 converges to 1.

Answer

(a)

(b)

(c)

Answer

Look at the sequence of integrals

as b gets larger:

These values are getting closer and closer to 1.

As b approaches ∞,

approaches 1. This means

converges to 1.

Each integral in the above exercise is the area between the graph of  and the x-axis on an interval with left endpoint 1.

As b approaches ∞, the area

approaches the total area between the graph of 

and the x-axis on the interval [1,∞).

In symbols, the total area between  and the x-axis on [1,∞) is

We abbreviate this limit by writing

Answer

a.

b.

c.

Answer

Look at the sequence of integrals

as the lower limit of integration b gets closer to 0:

These values are getting closer to 2.

As b approaches 0,  approaches 2. So

converges to 2.