Math 1411: Test 4
Directions: Show all of your work on this exam. An answer with no supporting work or explanation will not be given any credit.
1.
Find an antiderivative 
with 
and 
when 
2.
Use the Fundamental Theorem of Calculus to evaluate 
.
3.
Find the exact area of the region between 
and 
.
4. Find the area between the x-axis and the graph of the function
for one cycle of
the graph.
5. Find the general solution of the differential equation
.
6. An object falls from the top of a 400-foot building. When does it hit the ground and how fast is it going at the time of impact?
7. Find antiderivatives for the following functions. Check by differentiating.
a) 
b) 
where a is a constant
8. Find antiderivatives for the following functions. Check by differentiating.
a) 
, a is constant.
b) 
9. Is
the statement 
a true statement or a false statement?
Explain.
10. Is the statement “If a function is concave up, then the left-hand Riemann sums are always less than the right-hand Riemann sums with the same subdivisions, over the same interval.” a true statement or a false statement? Explain.
Back to the Calculus Page