MATH 116 PRACTICE MIDTERM 2

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Printable Key

PROBLEM 1  Integrate the following functions

A)  

Solution                     

B)   

Solution      

C)                  

Solution

PROBLEM 2  Find the area of the region bounded by the curve

        y  =  x3 - 3x2 - 4x  

and the line

        y  =  6x

  Solution

PROBLEM 3  Approximate the following integral using the midpoint rule with n  =  4 :

       

  Solution

PROBLEM 4  The revenue R in thousands of dollars at time t years after 1990 of a travel agency can be modeled by the equation  R(t)  =  t2 + t e-t .  Find the total revenue of the company from 1990 to 2000.

  Solution

PROBLEM 5  Set up the integral to find the volume of the solid that results when the region bounded by the curves

         y  =  3 - x  and y  =  3 + x - x2 

is revolved about the x-axis.  You do not need to evaluate the integral.

  Solution