Indefinite Integration Questions and Answers

Find the length of the curve 2t 1 3 2 3 X 2 2 y 0 t 12 The length of the curve is Simplify your answer

Find the length of the curve x t y 1 2 0sts 3 The length of the curve x t y 2 on 0sts 3 is is 0 Type an integer or a fraction

Let f 0 sin 0 3 cos 0 Calculate the derivative Note to get the to show up type theta and the system will immediately convert the word to the symbol f 0 cos 0 3 sin 0 List the first interval after 0 where both endpoints of the interval are critical numbers of the function on which f is increasing Increasing List the first interval after 0 where both endpoints of the interval are critical numbers of the function on which f is decreasing Decreasing

27 Find the exact area under y 5te for 0 t 6 NOTE Enter the exact answer Area

Given the function f x x e7 Use the derivatives to determine the open interval s where the function is concave up algebraically Leave answers in exact form Determine the open interval s where the function is concave down Determine any points of inflection

a Send a survey home with every student and ask parents to fill it out and return it the next day Which kind of sampling strategy is involved This question 2 point s possible In a large city school system with 21 elementary schools the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade The PTA wants to find out whether parents agree with this plan Listed below are some of the ideas proposed for gathering data For parts a through d indicate what kind of sampling strategy is involved and what if any biases might result Assume the schools are homogeneous and differ from each other OA An attempt at a census OB Systematic sampling OC Convenience sampling OD A simple random sample What kind of bias if any is most likely to result OA Response bias could result since the PTA wants parents to agree to this plan OB Undercoverage bias could result since only parents involved with the PTA will be sampled Submit test

Find the numerical value of each expression Round your answers to five decimal a cosh In 9 b cosh 9

qual x 2x 8x 32x 128 0 system Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the once OB The solution set is

Which of the following can be converted to the form a b I c COS X 2 sinx 1 d 2x 1 x2 x 1 x 1 1 e ex ex 2 dx dx dx dx n 1 1 19 W dx dw using a substitution

Indicate whether substitution is appropriate for each of these integrals If so evaluate the integral and enter the answer in the box that appears a fasina sin dx Choose one b fa sin sina da Choose one

Find the integral given below Check your answer by differentiation e 14e 148 e e 148 da C

eve gral given below Check your answer your answer by differentiation C

Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimu Select all that apply Of x x over 2 2 g x x over 1 1 Oh x ln x over 0 3 j x x over 1 1

Consider the function g x x 3x10 2 Use the second derivative test to find the x coordinates of all local maxima If there are multiple values give them separated by commas If there are no local maxima enter

Find the area bounded by the given curves y 4x 1 and y 4x 1

4 Find an antiderivative of the given function a f x x x b f x 3e2x x 1 x d f x 2 cos x e f x sin 3x x

2 1 point Write 3 different equations f x g x and h x such that 2 f x g x h x x

where b is a real constant Use Desmos to graph this function with a slider for b Guiding Questions 1 What do you notice about how the slope of the function changes with b What does this tell us about how addition or subtraction of constants impact the behavior of functions How does this related to the graph transformations you reviewed in week 1 of the course 2 Now that you have a sense for the function s behavior pick two distinct points a b in the function s domain such that f a f b If the MVT holds what feature must be present in the function for some twith a x b How can we use this observation to get a better

The Kardashi B O A Failed to ope B f x 4 0 66 8 f x 2 0 66 e f x 4 1 32 a f x 2 0 89 e f x 2 1 32 8 f z 2 1 58 AC a A b B C C d D e E f F New Apple iP D Weedmaps E F Welcom

27 28 Find the antiderivative F of f that satisfies the given condition Check your answer by comparing the graphs of f and F 27 f x 2e 6x F 0 1

Find the exact value of the expression belo cos sin Oa0 Ob 3 b 001 12 200

ose that you earned a bachelor s degree and now you re teaching high school The school ct offers teachers the opportunity to take a year off to earn a master s degree To achieve goal you deposit 5000 at the end of each year in an annuity that pays 6 compounded Jally How much will you have saved at the end of five years Find the interest Click the icon to view some finance formulas Formulas In the following formulas P is the deposit made at the end of each compounding period r is the annual interest rate of the annuity in decimal form n is the number of compounding periods per year and A is the value of the annuity after t years 371 A P 1 r 1 r A P a After 5 years you will have approximately Do not round until the final answer Then round to the nearest dollar as need nt In the following formulas P is the principal amount deposited into an account ris the annual interest rate in decimal form n is the number of compounding periods per year and A is the future value of the account after t years 0 P 1 r A P 1 X

The instantaneous rate of change of the value of a certain investment P is proportional to its value That is to say TP If r 7 and P 0 4500 P t

If you choose to not do these problems please do not turn in the assignment 1 extra credit 10 pts Consider the function of two variables given by 1 f x y x y x yl Experiment with fon scratch paper for various real number inputs in place of 2 x and y Show two of the calculations below and briefly explain what this function does

Describe the graph of fit f 0 1 and f x 3 for x

Find the derivative of 6 O In 6 6 O In 6 6 O 6 In 6

Sud udv uv va Seec 3x dx

Differentiate f x the function f x sin 7 In x 7 cos 7 ln x

Edmundo used a number line to show the solution for the inequality 12x 61 4 Which number line shows the solution O 6 5 4 3 2 1 0 1 2 3 4 5 6 6 5 4 2 1 0 1 2 3 4 5 6 8 5 4 3 2 1 0 1 2 3 4 5 6 6 5 4 3 2 1 0 1 2 3 4 5 6

Integral 7 O secz tan a

Evaluate the indefinite integral 6x4 75 3 dr C

Evaluate the indefinite integral 8 dx C

the domain and the range for the function Q Q 10 10 S ID OA D 0 5 R 5 OB D 00 00 R OC D 0 5 R 0 OD D 0 00 R x

llow the steps for graphing a rational function to graph the function R x Simplify your answer Type an ordered pair Use a comma to separate answers as needed OB The graph of R intersects the horizontal or oblique asymptote at infinitely many points OC There is no point at which the graph of R intersects the horizontal or oblique asymptote D There is no horizontal or oblique asymptote Use the real zeros of the numerator and denominator of R to divide the x axis into intervals Determine where the graph of R is above or b evaluating R there Select the correct choice and fill in the answer box es to complete your choice A The graph of R is above the x axis on the interval s 13 6 0 and below the x axis on the interval s 13 6 0 Type your answers in interval notation Use a comma to separate answers as needed x 6 X X 13 OB The graph of R is above the x axis on the interval s Type your answer in interval notation Use a comma to separate answers as needed OC The graph of R is below the x axis on the interval s Type your answer in interval notation Use a comma to separate answers as needed Use the results from the previous steps to graph R Choose the correct graph SOA Q O B Q O C

x 125 64 Follow the steps for graphing a rational function to graph the function H x OA The function has one horizontal asymptote Type integers or simplified fractions Use a comma to separate answers as needed Type each answer only once B It approaches either o or o on both sides of the asymptote s at x Type integer or simplified fraction Use a comma to separate answers as needed Type each answer only once C It approaches o on one side of the asymptote s at x 8 8 and o on the other Type integer or simplified fraction Use a comma to separate answers as needed Type each answer only once OD There is no vertical asymptote Determine the horizontal asymptote s if any exist Select the correct choice and if necessary fill in the answer box es to complete your choice Type an equation Use integers or fractions for any numbers in the equation OB The function has two horizontal asymptotes The top asymptote is and the bottom asymptote is Type equations Use integers or fractions for any numbers in the equations C The function has no horizontal asymptote Determine the oblique asymptote s if any exist Select the correct choice and if necessary fill in the answer box es to complete your choice OA The function has one oblique asymptote Type an equation Use integers or fractions for any numbers in the equation OB The function has two oblique asymptotes The oblique asymptote with a negative slope is and the oblique asymptote with a positive slope is Type equations Use integers or fractions for any numbers in the equations OC The function has no oblique asymptote

b Use a calculator or computer to find Lexd Round your answers to three decimal places dx i e x6 dx i L e dx er Led i dx i affe eTextbook and Media c The improper integral e to dx for a 1 a 2 a 3 a 7 Round your answer to three decimal places 4 e x dx converges to a finite value Use your answers from part b to estimate that va

Follow the steps for graphing a rational function complete your choice A R x B R x cannot be factored further graph the function R x OA R x Type your answer in factored form Do not simplify X 6 x x 13 What is the domain of R x 13 U 13 0 U 0 00 Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression Write R x in lowest terms Select the correct choice and if necessary fill in the answer box to complete your choice Simplify your answer B R x is already in lowest terms Locate the intercept s of the graph Select the correct choice and if necessary fill in the answer box es to complete your choice OA The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s A and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither an x intercept nor a y intercept

Solve the inequality R x 0 where R x 6 x 2 6 4x 4 3x 6 by using the graph of the function I The solution set for R x 0 is Type your answer in interval notation

Evaluate the integral sin x dx C 3

Evaluate the integral S tan 11x sec 11x dx Stan 11x00 111

Find the limit of the rational function a as x o and b as x co Write co or co where appropriate f x 3 x 3 a lim x 3 3 X X 5 b lim X 5 x x 3 3 YmX 5 11 Simplify your answer Simplify your answer

Express the integrand as a sum of partial fractions Select the correct choice below and fill in any answer boxes to complete your choice Use integers or fractions for any numbers in the expression A OB U S X 4 2 x 9x 10 X 4 x 9x 10 S dx X 4 x 9x 10 Evaluate the integral x 4 x 9x 10 dx dx dx S S S 6 11 x 10 X 4 X 4 2 x 10 5 11 X 1 Ws dx dx 2 X 1 dx

Use any method to evaluate the integral 30 dx S 225x 1 30 dx 225x 1 S 0

Evaluate the integral 169 t dt 169 1 dt Type an exact answer using radicals as needed

Use any method to evaluate the following integral 2 S 0 2 S 3dx 3 16 x 3dx 3 2 II 16 x Type an exact answer using radicals as needed

Evaluate the integral 16 12 dt 16 F dt dt Type an exact answer using radicals as needed

Use any method to evaluate the integral x dx 3 x dx 3 2 2 x 49 X 49

Use any method to evaluate the integral x dx 3 S x 2 S x 16 x dx X x 16 2

A spherical weather balloon is being inflated The radius of the balloon is increasing at the rate of 2 cm s Express the surface area of the balloon as a function of time t in seconds Let S 0 0 S t cm

K Let P t be the population in millions of a certain city t years after 2015 and suppose that P t satisfies the differential equation P t 0 04P t P 0 7 a Use the differential equation to determine how fast the population is growing when it reaches 9 million people b Use the differential equation to determine the population size when it is growing at a rate of 800 000 people per year c Find a formula for P t a Choose the correct process to find how fast the population is growing when it reaches 9 million people OA Evaluate P t 0 04 9 OB Solve 9 0 04P t for P t OC Solve P 9 0 04P t for P t OD Evaluate P t 0 04P 9 C The population is growing at about million Type an integer or decimal rounded to two decimal places as needed b Choose the correct process to find the population size when it is growing at a rate of 800 000 people per year OA Evaluate P t 0 04P 0 8 OB Solve P 0 8 0 04P t for P t OC Solve 0 8 0 04P t for P t O D Evaluate P t 0 04 0 8 when it reaches 9 million people The population size is about million Type an integer or decimal rounded to two decimal places as needed when it is growing at a rate of 800 000 people per year