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. PROBLEM 1 Integrate the following functions A) B) C)
PROBLEM 2 Find the area of the region bounded by the curve y = x^{3}  3x^{2}  4x and the line
y = 6x
PROBLEM 3
Approximate the following integral using the midpoint
rule with n = 4
:
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) = t^{2} + t e^{t}
. Find the total revenue of the
company from 1990 to 2000.
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  x^{2}
is revolved about the xaxis. You do not need to evaluate the integral.
