All our Essay orders are Original, and are written from scratch. Try us today at 30% off


Math 131 Fall 2021 Exam 1
Make sure to show all work to receive full credit for each question. Answers without supporting work will receive a score of zero. Also, please box your final answers, do your best to write clearly and legibly, and write your name on every odd-numbered page.
Multiple Choice / Short Answer
1. (1 pt each) Below are 4 graphs, each illustrating a Riemann Sum.
(a) (b)
(c) (d)
Match the graph above with its Riemann Sum below.
5∑ i=1
f(xi−1) ∆x 5∑ i=1
f(xi) ∆x 5∑ i=1
f(x̄i) ∆x 5∑ i=1
f(x∗i ) ∆x
2. (6 pts) Circle the letter next to each statement that is always true.
(a) ∫ cf(x)dx = c
∫ f(x)dx where c is a constant
(b) ∫
[f(x)g(x)] dx = (∫
f(x)dx )(∫
g(x)dx )
(c) ∫ c a f(x) dx +
∫ b c f(x) dx =
∫ b a f(x) dx
(d) ∫
f(x) g(x)
dx = ∫ f(x)dx∫ g(x)dx
(e) ∫
[f(x) ±g(x)] dx = ∫ f(x)dx±
∫ g(x)dx
(f) ∫ b a f(x)dx = −
∫ a b f(x)dx
/ 10 pts

3. (1 pt) The function f(x) = sin(x) is continuous on what interval?
(a) [−π,π] (b) [0,π]
(c) [−π, 0] (d) (−∞,∞)
4. (1 pt) Circle the phrase that best completes the statement below:
The equation
∫ x=1 x=−1
ln(x) dx = [x ln(x) −x]x=1x=−1 is
(a) correct by the Fundamental Theorem of Calculus Part II.
(b) incorrect because the antiderivative of f(x) = ln(x) is F(x) = 1 x
, not x ln(x) −x. (c) incorrect because 1
x is discontinuous at x = 0.
(d) incorrect because ln(x) is discontinuous on [−1, 0].
5. (2 pt each) Match the expression on the left with its definition on the right.
∑n i=1 f(xi) ∆x
lim n→∞
∑n i=1 f(xi) ∆x
(a) a + i∆x
(b) ∫ b a f(x) dx
(c) ith subinterval midpoint
(d) Net area sum of n approximating rectangles
(e) b−a n
(f) ith subinterval sample point
(g) ith subinterval left endpoint
6. (2 pts) Consider points C and D. One is the centroid of the shaded region; the other is the average midpoint of n approximating rectangles as n → ∞. Label each point, and briefly explain your choices in the section below right.
/ 18 pts

7. (10 pts each) Solve both integrals:
(a) ∫ [
1 x3
+ cos(2x) + 1 x
] dx (b)
∫ e √ x dx
/ 20 pts

8. (10 pts) Choose either (a) or (b) below to solve. Do not solve both.
(a) ∫ 2π 0
sin( 1 3 x)2 dx
/ 10 pts

(b) ∫
2×2+2 2×2+5x+3
/ 10 pts

9. (10 pts) Chose either (a) or (b) below to solve. Do not solve both.
(a) A particle moves along a line with velocity function v(t) = t2−t, where v is measured in meters per second. Find the displacement and the distance traveled by the particle during the time interval [0, 5]
/ 10 pts

(b) Find the centroid of the region bound by and f(x) = −x2 + 4 and the x-axis
To receive full credit: 1) Graph the region below; 2) Locate and graph the points of intersection of f and the x-axis; 3) Find the coordinates of the centroid and graph it below.
/ 10 pts

A bucket that weighs 4 lbs and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is filled with 40 lbs of water and is pulled up at a rate of 2 ft/sec, but water leaks out of hole in the bucket at a rate of .2 lbs / sec. Find the work done in pulling the bucket to the top of the well.
10. (1 pt) If F measures force and d distance, circle the equation below that measures Work (W ):
(a) W = F d
(b) W = Fd
(c) W = F + d
(d) W = F −d
11. (1 pt) The units of force acting on the water and bucket as it rises to the top of the well are
(a) Newtons (N)
(b) Joules (J)
(c) Pounds (lbs)
(d) Foot-Pounds (ft. – lbs)
12. (1 pt) The units of work required to lift the bucket and water to the top of the well are
(a) Newtons (N)
(b) Joules (J)
(c) Pounds (lbs)
(d) Foot-Pounds (ft. – lbs)
13. (1 pt) Choose the answer that best fills in the blanks.
As the bucket and water move up the well, the force acting on bucket is because its weight is , but the force acting on the water is because its weight is .
(a) constant, constant, changing, changing
(b) constant, changing, changing, constant
(c) changing, constant, changing, constant
(d) changing, changing, constant, constant.
14. (3 pts) Based on your answer to 13 above, calculate the work W needed to haul the bucket alone from the bottom to the top of the well.
/ 7 pts

Now, let’s figure out the work required to haul the water all the way up the well.
15. (1 pt) If t is measured in seconds, which expression is equal to the weight in lbs. of the water in the bucket at time t as it moves up the well?
(a) 40 .2t
(b) 40(.2t)
(c) 40 + .2t
(d) 40 − .2t
16. (1 pt) If x is a measure of feet, which expression gives the distance of the water in the bucket from the bottom of the well at time t?
(a) x = 2 t
(b) x = 2t
(c) x = 2 + t
(d) x = 2 − t
17. (2 pts) Use your answers to questions 15 and 16 above to define an expression for the weight of the water in terms of x.
Scratch work to help you with Questions 15 and 16. Not necessary to use, not counted for credit!
/ 4 pts

To find the work W required to haul the water 80 ft up the well, we start by subdividing the 80 ft interval into n equally spaced subintervals of ∆x feet.
When ∆x is very small, the weight of the water is relatively constant throughout the length of the interval.
18. (2 pts) Define an expression that approximates Wi, the work required to lift the water a distance of ∆x feet, from xi−1 to xi.
By summing up all the W ′is, we can approximate the work needed to haul to water from the top to the bottom of the well.
19. (2 pts) Write an expression for the sum of all the W ′is.
We can make this approximation precise by letting n →∞ and then taking the limit.
20. (4 pts) Write an expression that calculates the precise amount of work needed to haul the water from the bottom to the top of the well, and then solve it.
21. (1 pts) Use your answers to Questions 14 and 20 to calculate the total amount of work needed to haul the water and bucket from the bottom to the top of the well.
/ 8 pts

Extra Credit: (3 pts) Which of the following areas are equal? To receive credit, your answer must be justified by the correct explanation.
(e) (f)
/ 3 pts

The post Math first appeared on Assignment writing service.



Great Job

Great job! Those were you, guys, who made my coursework perfect in time according to all my requirements. I will...

Best Service

The book review I asked for is so amazing! Endless thanks to your team for completing my review and for...


They look cool and trustworthy enough to me. I gather they made discounts as their prices are quite affordable if...

Comes through every time

I have used this website for many times, and each time they found perfect writers for me and they produce...

Mh! not bad…

The worst part ever was to find my deadline postponed for 1 hour ! They couldn`t finish the essay within...

No Complaints So far Guys

Yeah …I really like all the discounts that they offer, the prices are very flexible. Plus they have different promotions...

CLICK HERE  To order your paper

About Scholarfront Essay writing service

We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.

How It Works

To make an Order you only need to click on “Order Now” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.

Are there Discounts?

All new clients are eligible for upto 20% off in their first Order. Our payment method is safe and secure.

 CLICK HERE to Order Your Assignment



Let your paper be done by an expert

Custom Essay Writing Service

Our custom essay writing service has already gained a positive reputation in this business field. Understandably so, all custom papers produced by our academic writers are individually crafted from scratch and written according to all your instructions and requirements. We offer Havard, APA, MLA, or Chicago style papers in more than 70 disciplines. With our writing service, you can get quality custom essays, as well as a dissertation, a research paper, or term papers for an affordable price. Any paper will be written on time for a cheap price.

Professional Essay writing service

When professional help in completing any kind of homework is all you need, is the right place to get it. We guarantee you help in all kinds of academia, including essay, coursework, research, or term paper help etc., it is no problem for us. With our cheap essay writing service, you can be sure to get credible academic aid for a reasonable price, as the name of our website suggests. For years, we have been providing online custom writing assistance to students from countries all over the world, including the United States, Canada, the United Kingdom, Australia, Italy, New Zealand, China, and Japan.