Definite Integrals Questions and Answers

Find the length of the curve x J4 8 1 4y2 1 y 2

Write the expression in the standard form a bi 3 8i 1 9i 3 8i 1 9i Simplify your answer

3 10 points Find the Taylor series of the function e2r 5 around x 3

4 a 9 points Determine whether the following improper integral or divergent de xe is convergent

b 9 points Evaluate the integral sin In x dx

ion 4 e that f is a function given as f x 2x 5 y the expression f x h h f x h f x h y the difference quotient h f x h alize the numerator in the difference quotient If a h f x

Moments of Inertia In Exercises 59 and 60 set up a triple integral that gives of density p the moment of inertia about the z axis of the solid region 59 Q x y z 1 x 1 1 y 1 0 z 1 x p x y y

te S x y z dS where S is the part of the cone 2 x y that lies between the planes Evaluate z 1 and z 4

5 Row reduce the following matrices to reduced row echelon form and list the pivot columns Confirm your answers in MATLAB using the command rref a 1 3 0 4 6 0 0 1 0 6 0 0 0 0 0 0002 2 b 1 0 1 0 0 0 1 0 1 0 0 0 4 0 2 0 0 0 2 1

Suppose that 0 5 A f f 21 dt B f t dt 19 Calculate each of the following 0 125 f 1 8t dt 0 5 c f 4 8t dt 0 375

Evaluate the integral 7 sin x cos x dx Note Use an upper case C for the constant of integration 2

Find the area of the part of the paraboloid x y 2 for C 0 x 4

5 log r da using b 4 marks Let T denote the trapezoidal rule approximation for subintervals of length Ar 1 Write T as a sum in simplified form

now that T S 0 sin x 1 cos x dx FIN 2 Justify your answer fully

Ms Smyth 78 years old had lived in the same home for 30 years Never married she cared for her disabled mother for 15 years After her mother died she lived alone on a small pension She appeared to be well groomed and appropriately dressed when she left her house Ms Smyth was hospitalized for a bowel obstruction and Joe a community health nurse made a follow up visit after discharge to her home When Joe arrived at the house he was overcome with the smell of rotting garbage urine and feces Five small dogs ran back and forth among piles of garbage and magazines overturned furniture and discarded appliances There was no running water and the bathroom was not functional Joe told Ms Smyth that her living conditions were unhealthy and that he would contact a community agency to help her clean her house Ms Smyth became very angry and said no one had the right to take her things away Is it ethical for Joe to overrule Ms Smyth s autonomy in decision making What action is in Ms Smyth s best interests What action is in the community s best interests What ethical issues are involved in caring for a client with a hoarding disorder such as that seen in Ms Smyth s situation

Nancy Corbin s regular hourly wage rate is 18 and she receives an hourly rate of 27 for work in excess of 40 hours During a January pay period Nancy works 45 hours Nancy s federal income tax withholding is 96 she has no voluntary deductions and the FICA tax rate is 7 65 Use January 15 for the end of the pay period and the payment date Prepare the journal entries to record a Nancy s pay for the period and b the payment of Nancy s wages Round Intermediate calculation and final answers to 2 decimal places eg 15 25 Credit account titles are automatically indented when amount is entered Do not indent manually No Date Account Titles and Explanation a bl Jan 15 Jan 15 Debit Credit

Stap 2 of 2 Find the domain How to enter your answer ope

Let f x cos x Approximate the integral I f z dz in three different ways each with n 4 a a Right Riemann Sum b the Trapezoidal Rule and c Simpson s Rule Give each answer correct to six decimal places a R b T c S4 It can be shown that for each z in 0 1 z 4 and f z 43 Combine these facts with the error control inequalities discussed in class to complete the following guarantees concerning the absolute errors in the approximations from parts b a Give each answer correct to six decimal places d I Tel e I Sal Using the facts given for parts d and e and the error formulas find the smallest integer n for which we can guarantee that the approximation T is within 107 of the exact value a Repeat for S 1 For T n g For S n Which wo su rath

The rectangles in the figure below illustrate a right endpoint Riemann sum for f x The value of this right endpoint Riemann sum is the z axis and the vertical lines z 2 and r 6 8 1 2 2 9 3 on the interval 2 6 and this Riemann sum is greater than 6 7 Right endpoint Riemann sum for y on 2 6 8 the area of the region enclosed by y f x

Consider the integral I 1 1 1 sin x 5 dx a Approximate I using the Trapezoid Rule with n 6 subintervals T6 b Approximate I using Simpson s Rule with n 6 subintervals S6

Company A showed a profit of 1 3 million last year The CEO of the company expects the profit to increase by 7 each year over the next 5 years and the profits will be continuously invested account bearing a 4 25 APR compounded continuously a Write the flow rate R of the income stream Let t represent the number of years after the company showed a profit of 1 3 million R t million dollars per year b Calculate the 5 year future value Round your answer to three decimal places million c Calculate the 5 year present value Round your answer to three decimal places million

Use both the Trapezoidal Rule and Simpson s rule to estimate the integral 8 In both cases use all the information in the following table of values for f 15 x 2 3 4 5 6 7 8 f x 2 6 2 7 2 5 2 8 2 2 1 2 1 4 Trapezoid Rule approximation Tn Simpson s Rule approximation Sn f x dx

Estimate the area under the graph of f x 9 2 from z 1 to z 5 using a right Riemann sum with four approximating rectangles R Sketch the graph and the rectangles defining R4 then complete this statement the exact area A R is less than

3 Consider the PDE in u u x t Solve for u with data 3u uu 0 u t 0 3 1 for x 0 for 0 I

B2 Take S to be the set that is given by S x y x y 1 Take f to be the function that is given by x 2x 7x 5 s R Transform S to obtain a set E and f to obtain a set g by scaling the x axis by a factor of 5 and by scaling the y axis by a factor of 3 and then by translating the resulting sets by the vector 4 1 a Find an equation that describes E b Find an equation that describes g

L 2 where 2 x y exy dA is the region in the first quadrant that is enclosed by the hyperbolas x y 0 x y 1 xy 1 xy

equation x 3 c2 3 y 1 a Sketch the given curve and compute its length You are allowed to use a plotting program like Desmos for the visualization of the graph Utilize the symmetry of the curve when you compute its length b Compute the surface area of the surface obtained by revolving the given curve with y 0 1 about the Y

If f x sin x 2x 2 then f x 5x 4 cos x 5 2x 2 2 4x cos x 5 2x 2 2

Consider the indefinite integral a Then the integrand decomposes into the form C d az b where 9 b C d 3x 21 712 60 2 25 32 2 H 5 z 5 Integrating term by term we obtain that 32 21 71z 60 dz 22 25 dr

3 3 Consider the function f x x x 1 on the interval 1 00 Find the relative and absolute extrema Use the first derivative test if needed No graph is needed 12 Points

If you know that f 3 17 and then 3 0 se 0 f 0 de 3 f y dy 9

Determine whether the integral is convergent or divergent If it is convergent evaluate it If the quantity diverges enter DIVERGES Z L 77 36 dz

3 Find the area of the sector shown a b 80 8 0 5 rad 10

4 Find a parametrization for the curve The line through the points 3 3 and 5 1

da set of parametric equations for the line that passes through 3 4 and 5 6 ect one a x 3 5t y 4 6t b x 3 4t y 5 6t c x 3 8t y 4 2t d x 3 8t y 4 2t

e figure to solve each inequality

Find all solutions real or imaginary 6k 1 125 Choose the correct solution set bel OA F

in the blank quadratic function of the form f x ax form f x

Problem A random variable X has CDF 860 ft 70 Fx x e x x 0 4 0 x 0 Find P X 2 P X 0 P X 10 What kind of random variable is X

For a 4 unit class like Statistics students should spend average of 12 hours studying for the class A survey was done on 23 students and the distribution of total study hours per week is bell shaped with a mean of 14 hours and a standard deviation of 3 2 hours Use the Empirical Rule to answer the following questions a 68 of the students spend between hours and b 95 of the students spend between c 99 7 of the students spend between hours and hours and hours on Statistics each week hours on Statistics each week hours on Statistics each week

b Evaluate the integral 12 D where D x y x y 2 x tan x y 4 dA

Use the trapezoidal rule to approximate the area under the curve f x Submit an exact answer Provide your answer below 2x 2 4 on the interval 0 3 Use n

On your own paper plot these points Then use the information about the derivatives and the intervals to classify the point 5 7 as a Max Min Inflection Point or none of the 3 5 5 7 7 8 12 4 13 5 Graph the function using the info below BEFORE you answer the question Not all questions use the same graph Function is increasing on 0 7 decreasing on 7 00 Concave Down over 0 3 5 12 Concave Up over 3 5 12 00 Max Min none of these Inflection Point

HITS UT LINGUI K Question Solve the following system of equ a solution state whether the syst 3x 7y 25 2x 5y 22

Find a positive angle less than 2x that is coterminal with the given angle 25x 4 A positive angle less than 2x that is coterminal with 0 25 is

The Schwimmers cost for cable television is gi is the number of months of service Complete p Use the grapning tool to grapn the equation

Study the following diagram A worldwide network Microchip Used to store information O Integrated circuit Enovel Which of the following best completes the diagram Used to process information Used to share information

D D O Determine whether the graph represents a function If it does represen range 153 No What is the domain Select the correct choice below and if necessary your choice A

6 Determine with justification whether each of the following improper integrals converges or diverges a In x 1 00 C 5 e c f x S dx 1 x ln x d Se da where p is a positive real number 1 In x X da 1 x ln x dx In x dx da

Consider the following data regarding students college GPAS and high school GPAS The estimated regression equation is Estimated College GPA 0 84 0 5310 High School GPA Compute the sum of squared errors SSE for the model Round your answer to four decimal places GPAS College GPA High School GPA 2 11 2 73 4 35 2 30 3 84 2 17 2 73 3 84 2 47 Copy Data 4 99 4 80 3 66