Please see the attached file for the fully formatted problems.
Solve the initial value problem:
________________________________________dx = x^/¯(9+x2) ; y(-4) = 0
f(x) = x2+3
ni=1 f(xi) x
Given Figure 3.1, find the exact area A of the region under f(x) on the
interval [1, 3] by first computing Figure 3.2 and then taking the limit as
limn sin 
________________________________________4 + sin 2
________________________________________n + sin 3
________________________________________n + sin n
Evaluate Figure 4.1 by interpreting it as the
limit of Riemann sums for a continuous function f defined on [0, 1].
Given Figure 5.1, first sketch the graph y = f(x) on the given interval.
Then find the integral of f using your knowledge of area formulas for
rectangles, triangles and circles.
Suppose that a tank initially contains 2000 gal of water and the rate of
change of its volume after the tank drains for t min is V'(t) = (0.5)t - 30
(in gallons per minute). How much water does the tank contain after it
has been draining for 25 minutes?
Find an upper and lower bound for the integral (Figure 8.1) using the
comparison properties of integrals.
Apply the Fundamental Theorem of Calculus to find the derivative of:
y = 9-x2 , y=5-3x
Sketch the region bounded by the graphs of Figure 12.1, and
then find its area.
Approximate the integral (Figure 13.1); n=6, by:
a) first applying Simpsonfs Rule and
b) then applying the trapezoidal rule.
Find the mass M (in grams) of a rod coinciding with the interval [0, 4]
which has the density function
(x)= 5 sin 
The region R is bounded by the graphs
x-2y=3 and x=y2
Set up(but do not evaluate) the integral that gives the volume of the solid
obtained by rotating R around the line x = -1.
Find the volume of the solid that is generated by rotating the region
formed by the graphs of Figure 16.1 and y = 4x about the line x = 3.
Use the method of cylindrical shells to find the volume of the solid
rotated about the line x = -1 given the conditions:
y = x3 - x2; y = 0; x = 0
Find the length of the graph of
y = 1
________________________________________3 x3/2 - x1/2
(1, - 2
A 10-ft trough filled with water has a semicircular cross section of
diameter 4 ft. How much work is done in pumping all the water over
the edge of the trough? Assume that water weighs
y = x2
The region in the first quadrant bounded by the graphs of y = x and Figure 20.1 is rotated around the line y = x. Find
(a) the centroid of the region and
(b) the volume of the solid of revolution.
A variety of calculus problems are solved. The solution is detailed and well presented.