Definite Integrals Questions and Answers

44 Describe the graph of the equation 8 80 A a circle of radius 1 with center at the point 1 80 B a line passing through the pole making an angle of 80 with the polar axis OC a circle of radius 99 with center at the pole D a line perpendicular to the polar axis passing through the point 1 80

A bungee jumper s height h in feet at time t in seconds is given in part by the data in the table t h t 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 5 5 555555 41 09 57 11 77 92 100 119 98 135 11 143 64 8 144 93 8 5 139 49 9 128 75 9 5 114 8 10 100 a Use the data to estimate 6 5 7 200 187 88 163 98 132 94 7 5 100 70 2 47 62 34 9 32 97 h 6 5 h 7 h 7 5 b At which of these times is the bungee jumper rising most rapidly at t 6 5 at t 7 att 7 5

Suppose that the position of a particle is given by s t 4 t 2 6t 9 a Use the limit definition of the derivative to find the velocity at time t v t b Find the velocity at time t 3 seconds m s m s a t c Use the limit definition of the derivative to find the acceleration at time t m s 2 d Find the acceleration at time t 3 seconds

D Oy 2 Question 18 A third degree polynomial f x H What would be one of

14 O 5 3 x 5 Question 9 let f x 3x 4x 1

7 pts With the aid of series prove that if f z COS Z 2 x 2 1 when z 2 2 when z then f is an entire function Also write the first three terms of the seri representation

he amount that results from th 94 con ounder

Evaluate the integral using the following values 8 8 x dx 960 x dx 24 dx 4 L 21 Sax x dx 5x

10 9 8 7 35 6 Based on the graph above estimate to one decimal place the average rate of change from 2 4

Use these rental pricing data to answer the questions below City 2009 Rent 2015 Rent Boise 583 745 Boston 1 577 2 150 Seattle 958 1 600 What is the rate of change of rent with respect to time for Boise Round to the nearest penny a specify units in the question below Answer What are the proper units for this rate of change years per dollar years dollars dollars per year

In the figure to the right the equation of the solid parabola is y x 2 and the equation of the dashed line is y x Determine the area of the shaded region OA JO OB S SIDS Set up the integral that will give the area of the region Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers dx Q G

Sketch the region and find its area The region bounded by y e y e3x and x In 3 Choose the correct graph below OA dx G dy CAMRY O C Q G OD Set up the integral that will give the area of the region Use increasing limits of integration Select the correct choice below and fill in any answer boxes to complete your choice Type exact answers COA S Q Q

9 01 Last week This week Seved Mikey is paid 16 40 per hour Last week he worked 40 hours and this week 60 hours Calculate Mike s pay for each week time and a half over 40 hours Note Do not round intermediate calculations Gross pay PRODE

Write an equation for the function graph a 7 a

with and e 8 n n 4 a Find the trapezoid rule approximations to the integral using 2n dx X 2n subintervals b Find the Simpson s rule approximation to the integral using 2 n subintervals c Compute the absolute errors in the trapezoid rule and Simpson s rule with

Suppose that and 2 are two forms on R such that m n dw where w is the one form w sin y z dx Let S be a surface in R3 whose boundary is a simple closed curve C that lies within the plane x 4 Show that m 7

ind the area of the region shown in the graph to the right y 3 x y 3 Q

csc In the figure to the right the equation of the solid curve is y 2 dashed curve is y 4 sinx Determine the area of the shaded region O Set up the integral that will give the area of the region Select the correct choice below and fill in the answer box to complete your choice Type an exact answer B S 5x S X dy and the equation of the dx GO Q Q G

7 The following are three different simulations to determine the experimental probability of having two children in a family both be girls Which is best to produce a more meaningful or significant probability and why 2 marks a A die is rolled 200 times a 1 is counted as a girl child a 2 is counted as a boy child all other numbers are ignored b A coin is tossed 150 times a heads is counted as a girl child a tails is counted as a boy child c A coin is tossed 300 times a heads is counted as a boy child a tails is counted as a girl child The best simulation is Explain why you chose your answer

Current Attempt in Progress Horatio Inc has three divisions which are operated as profit centers Actual operating data for the divisions listed alphabetically are as follows a Compute the missing amounts Operating Data Contribution margin Controllable fixed costs Controllable margin Sales Variable costs Textbook and Media Save For Later Women s Shoes 302 400 112 000 672 000 1 2 Men s Shoes 100 800 504 000 358 400 3 4 Children s Shoes Attempts 0 of 5 used 6 The parts of this question must be completed in order This part will be available when you complete the part above 201 600 106 400 280 000 Submit Answer

8 5 marks Determine if the following integral converges or diverges 2x Your answer must be fully intified p 03 X x5 5 dx

1 lim 6i 1 n i 1 n L lim Write down an integral with value L Justify your expression

2 11 Let f x f x 1 1 1 a 3 marks Calculate f 2 dt Answer

he gross domestic product GDP in trmans of dollars for Country A and Country B can be approximated as follows wher worresponds to the year 1960 Country Af x 0 00011 1 105 ountry B g x 0 0142 1 514 Ind the projected GDP in 2013 and 2027 for Country A Which of the following describes how to find the projected GDP in 2013 using the given information select the correct and fill in the answer box to complete your choice Type an integer or a decimal A To find the projected GDP in 2013 find the intersection point of the graphs y 0 00011 1 105 a The projected GDP in 2013 is represented by the y coordinate To find the projected GDP in 2013 substitute 113 for x and evaluate to find f x 2013 the projected GDP is about trillion Type an integer or decimal rounded to the nearest tenth as needed

7 Determine if the following integral converges or diverges 8 5 1 1 0 1 dr 1 2x If it converges find its value If it diverges determine if I o or I o or neither

Find all critical points of the following function f x y 8xy 2x 2y What are the critical points Select the correct choice below and if necessary fill in the answer box within choice OA The critical point s is are GREXI Type an ordered pair Use a comma to separate answers as needed OB There are no critical points

The graph below shows the sex ratio for different maternal ethnicities A sex ratio of one thousand represents an equal number of male and female births The minimum is from the year with the lowest sex ratio The maximum from the year with the highest sex ratio Which statement below correctly interprets the graph Race and Hispanic origin of mother Total White Non Hispanic white Black Non Hispanic black Mexican Central and South American Puerto Rican American Indian Chinese Filipino Cuban Minimum Maximum and Total Sex Ratio Reported by Race and Hispanic Origin of Mother 1 001 Japanese 985 Hawaiian 993 1 026 1 027 1 016 1 019 1 020 1 021 1 046 1 047 1 036 1 037 1 051 1 036 1 036 1 059 1 059 1 057 1 053 1 054 1 047 1 062 1 100 1 105 1 096 Legend Total sex ratio at line Minimum 1 128 Maximum 1 143

If cos 0 sin 0 1 and is in the 4th quadrant find the exact value for sin 0 5

Evaluate the triple integral ExydV where E is the solid tetrahedon with vertices 0 0 0 1 0 0 0 7 0 0 0 2

1 2 Points DETAILS LA Use a graphing utility to evaluate th

stion 4 bounded region shown for each problem repres he given cross sections Set up the integral s fir y x

Evaluate 152 dV where E is the region described by E 27 0 z 4 x y2 fullyroduced fraction such as 117 O O 0 15 ot

estion 4 p the integral that gives the volume o Set up the integral but do not evalu

Name SHOW WORK ON EACH PROBLEM FOR ANY PARTIAL CREDIT 10 pts each Go down deep enough into anything and you will find mathematics Dean Schlicter 3a Determine the linear approximation of f x at x a 7 and use it to approximate 15 99 9 x Show your steps 3b Use linear approximation or the differential to estimate 8 06 2 3 Show your steps

Exercise 16 Find the volume of solid Q that is the region bounded below by z 8 2 y and above by z 4x2 4y2 which inside the cylinder y 1

y csc x y cot x y cos x y sec x y sin x y tan x V 6 5 4 3 2 1 6 3 47 3 2 1 3 3 N 1 hime 55 COM

Solve the following inequality for x in 0 2m Use a table of signs or something similar to support your answer Do not use a graph x 5 x 2 e2x cos x 0

K Determine the length o The length of side A B

Find the general solution to the system x 2 1 x 1 2 2e t 3t

Show that the integral is independent of path and evaluate r 2 2 In 3 Ja 1 1 In 3 ez dx 3y dy 2xe z dz

Determine if da converges or diverges 3 converges to 1 9 O converges to 0 O None of the answer choices O converges to 1 18

b Explain why h x dx does not represent the area between the graph of y h x and th Sh x dx a Choose the correct answer below b A The shaded region is below the x axis so h x dx represents the negative of t

7 The graph of f is shown Evaluate each integral b interpreting it in terms of areas b f f x dx d f f x dx 0 2 a ff f x dx c ff x dx 5 D 0 YA 2 0 2 4 0 y f x D 6 8 X 0 0

41 For the function f whose graph is shown list the following quantities in increasing order from smallest to largest and explain your reasoning A fo f x dx B f f x dx C f f x dx D f x dx E f 1 YA 2 0 5 x

Evaluate the integral Answer 8x 32x 4 23 3x 4 1 dx Hint Factor the denominator by first finding a small integer root r Then use polynomial division to write Tr quadratic

Evaluate the integral K S 6x 24 x 8x 12

dx dy x y dx 5 xyy x 1 3 7 9 11 5x y e 1 y 2 cosx dp f p p 1 dt de dt 15 t sec 0 0e 2 dy 13 xe y 0 0 dx dA 8 4 xy y 3 6 y xe 0 dy dx 10 12 dx 14 Ab cos br A 0 b dr 16 x y k sec y y 1 6 dz dt dH dR 13 20 Find the solution of the differential equation that satisfies the given initial condition 4 dP dt 2x y 1 el z 0 RH 1 R In H Pt P 1 2 18 x 3y x 1 dx 20 0 19 x ln x y 1 3 y y dy x sin x dx y y 0 1 y 0 1 y 1 1 21 Find an equation of the curve that passes throug 0 2 and whose slope at x y is x y 22 Find the function f such that f x xf x x f 0 2 23 Solve the differential equation y x y by m change of variable u x y 24 Solve the differential equation xy y xe x change of variable v y x 25 a Solve the differential equation y 2x 1 b Solve the initial value problem y 2x 1 y 0 0 and graph the solution B c Does the initial value problem y 2x 1 y 0 2 have a solution Explain

ssion is used for y DETAILS nomotrie sub

Question 5 Find the equation of the slant asymptote of the rational function 2x 6x2 7x 10 f x 2x 5 The equation of the slant asymptote is y

Check nited Express a national pa dditional pound or fraction t urcharge for each additional