#### To determine

**To compute:**

The left and right Riemann sums for the given function on the interval *[0, 2]* with

*n=100*

#### Answer

*L100≈0.894691* and *R100≈0.908025*

*L100* is an underestimate and *R100* is an overestimate

#### Explanation

**1) Concept:**

Use a programmable calculator or computer and compute the left and the right Riemann sums for the given function on the given interval with the given value of *n*.

**2) Given:**

*fx=xx+1, 0, 2 and n=100*

*0.8946<∫02xx+1 dx<0.9081*

**3) Calculation:**

By using a programmable calculator it is obtained that

*L100≈0.894691* and *R100≈0.908025*, since *f(x)* is increasing on the given interval *0, 2*.

*L100* is an underestimate and *R100* is an overestimate. Therefore,

*0.8946<∫02xx+1 dx<0.9081*

**Conclusion:**

*L100≈0.894691* and *R100≈0.908025*

*L100* is an underestimate and *R100* is an overestimate

We have also verified that *0.8946<∫02xx+1 dx<0.9081*