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Midterm

MAT 145 Study Guide - Midterm Guide: Riemann Sum, Midpoint MethodExam


Department
Mathematics
Course Code
MAT 145
Professor
All
Study Guide
Midterm

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MAT 145 Term Test 5
2012 Spring
1. Determine the exact value of the definite integral (5 + 6+12
) .
2. A particle moves along the horizontal axis with acceleration ()= 2, 0 10. We also
know the initial velocity,
a) Determine v(t), a function for the velocity
b) Calculate the total distance traveled by the particle for 0 10.
3. If ()=cos(3)
, determine g’(x).
4. Evaluate 
.
5. We know that () =6, () =14,() =23.

Determine ().

6. Use Riemann Sum to approximate the area under the curve ()=
, 0    2, using n=4
subdivisions and the midpoint method. Round to the nearest thousandth.
7. Let g(t) represent a child’s rate of growth in pounds per year. Write a definite integral to
represent the change in the child’s weight, in pounds from year 4 to year 9.
8. An animal population is increasing at a rate of ()= 4 + 29 animals per year, t measured in
years. By how many animals does the population increase from year 3 to year 7?
9. A particle moves along the horizontal axis with velocity ()= 3 3, 0 6, measured in
ft/s. Determine the net change in position of the particle on 0≤t≤6.2
10. We wish to create a Riemann Sum to approximate the area under the curve =+ 2, 1
2, using n=4 subdivisions and the left-endpoint method.
a) Create a picture to show the function and the approximating rec tangles. Clearly label
the elements of your picture, including the function the horizontal axis scale, any x-axis
tick marks and your rectangles.
b) Write an expression, showing all terms, to represent the Reimann Sum.
c) Calculate the exact value, expressed as a common fraction, for this Riemann Sum.
Bonus!
Let R be the first-quadrant region bounded by the x-axis, the y-axis, and the graph of = 4  .
Determine the smallest number of subdivisions we must use in a left-endpoint Riemann Sum in order
to approximate the actual area of R with error no more than 0.01. Describe your process, justification
and results.
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