Problem 86AE

Riemann sums to integrals Show that in the following steps.

a. Note that n! = n(n − 1)(n − 2) ··· 1 and use ln (ab)=ln a + ln b to show that

b. Identify the limit of this sum as a Riemann sum for . Integrate this improper integral by parts and reach the desired conclusion.

Solution:-

Step1

To find

Show that in the following steps.

a. Note that n! = n(n − 1)(n − 2) ··· 1 and use ln (ab)=ln a + ln b to show that

b. Identify the limit of this sum as a Riemann sum for . Integrate this improper integral by parts and reach the desired conclusion.

Step2

a. Note that n! = n(n − 1)(n − 2) ··· 1 and use ln (ab)=ln a + ln b to show that

L=

=

=

L=

=

=

=

=

Hence,

L=

Step3

b. Identify the limit of this sum as a Riemann sum for . Integrate this improper integral by parts and reach the desired conclusion.

=

=

=

=

= -1

Hence

L===-1