Value of each definite integral
Not what you're looking for?
Name __________________________
Math 331
Fall 2015
DIRECTIONS: Show as much work as possible within each question as I grade on both the process and the final answer. TI-89's are wonderful calculators, but they don't show me if you know anything about calculus! Show all work.
1. (6 pts each) Determine the following antiderivatives (don't worry about simplifying, just show the rules)
a.
b.
c.
2. (6 pts each) Calculate the value of each definite integral (Show work!):
a.
b.
c.
3. (6 pts each) a. Approximate the area under the curve and above the x-axis by splitting the region from to into 4 equal subintervals (rectangles) and using the midpoints of the subintervals as the heights.
b. Use the Simpson's Rule with to estimate area under the curve
c. Find the exact value of , and compare with the answer obtained from part (a), and (b). Which method is more accurate, part A or part B?
4. (8 pts) Determine the area between the curves and
5. (6 pts) Use geometry to determine the value of the following definite integral:
6. (8 pts) A stock analyst plots the price per share of a certain stock as a function of time and finds that it can be modeled by the function where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first 2 years of its purchase.
7. (8 pts) Use the consumer's surplus formula to determine the consumer's surplus for the demand equation if we assume supply and demand are in equilibrium when
8. (8 pts) Sketch the region and then calculate the volume of the solid of revolution formed by rotating the region bounded by , , and around the x-axis.
9. The function represents the rate of flow of money in dollars per year. Assume a 8-year period for t and a rate r of 10% compounded continuously and determine the following:
a. (6 pts) The present value
b. (2 pts) The accumulated amount
Purchase this Solution
Solution Summary
The solutions are provided in a jpg file. Step-by-step computations are shown.
Education
- MSc, California State Polytechnic University, Pomona
- MBA, University of California, Riverside
- BSc, California State Polytechnic University, Pomona
- BSc, California State Polytechnic University, Pomona
Recent Feedback
- "Excellent work. Well explained."
- "Can you kindly take a look at 647530 and 647531. Thanks"
- "Thank you so very much. This is very well done and presented. I certainly appreciate your hard work. I am a novice at statistics and it is nice to know there are those out there who really do understand. Thanks again for an excellent posting. SPJ"
- "GREAT JOB!!!"
- "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts