Indefinite Integration Questions and Answers

Find the indefinite integral using integration by parts with the given choices of u and dv Use C for the constant of integration x 16 x In x dx u In x dv x dx 4 lnx 1 C

Solve the following integro differential equation t u y u du t y 0 0 y t

1 Compute the integral f 1 1 25x dx

Evaluate the indefinite integral x 4 2 x 8x S dx

10 Compute the integral xe x dx

Determine the graph of the hyperbolic paraboloid 2 y x x 36z Choose the correct graph of the hyperbolic paraboloid OA O C X X z Y S h OB OD X X N N y

Step 1 x cos 8x dx To find the indefinite integral Let u 8zx The differential of u with respect to x is du 167 Step 2 Rewrite the integration in terms of u 1 Apply the constant multiplication rule on the right side 1 x cos 8x dx use the trigonometric identities x cos 8x dx cos U 16 Step 3 Integrate the right side 15 cos 16 cos u du 16 sin u 16 16T cos u du sin u C 16T 3 16 T du Step 4 Substitute the expression for u on the right side and obtain the integral 16 T x d

Find the equation of the line shown below Your answer should take the form x a or y a whichever is appropriate 45 4 3 2 1 5 4 11 3 2 1 1 2 3 4 5 2 3 4 5 www H

D 3 x 2 ay Transform D to cylindrical and spherical coordinates

What is the partial fraction decomposition of f A B C D B Cx D E x 2 x 2 x 2x 1 x 1 Ax B Cx D 2 x Ax B 2 x 2 2 x E 2 x 2x 1 Cx D 2 x B 2 x Ex F 2x x 1 B Cx D 2 x 2 x Cx D Ex F 2 x 2x x 1 F x 1 5x 13 2 x 2 x 2x x 1 dx

Simplify y 4 y 8 Write your answer with a positive exponent only

Find the derivative f x 20x 2 1x20 OA 10x 1 2 10x19 OB 10x1 2 10x19 O c 10x 1 2 10x10 D 10x 2 10x10

2 Evaluate each integral a f3 sec x sec x tan x dx

Coal gas is produced at a gasworks Pollutants in the gas are removed by scrubbers which become less and less efficient as time goes on The following table gives R t the number of kilograms of pollutant per month captured by the scrubbers Let t be the number of months since the scrubbers were installed t R t Estimate 36 37 95 33 95 35 95 1 15 8 4 1 5 14 6 2 13 2 2 5 12 1 3 10 9 3 5 9 3 R t dt using a Trapezoidal rule with 6 intervals 4 7 8

The graph of y f x is shown in blue Draw the graph of y 2f x shown in red by determining how a stretch or compression will transform the location of the indicated blue points Drag the movable red points to the desired coordinates Provide your answer below 124 11 10 9 18 7 6 940 3 8 66 6 6 7 8 9 49 10 11 12

39 Demand The daily demand x for a certain product in hundreds of pounds is a random variable with the probability density function f x 343x 7x 0 7 a Find the mean and standard deviation of the demand b Find the median of the demand c Find the probability that the demand is within one standard deviation of the mean

If we know that fr 1 f t dt sin t t C evaluate Safe R 2 f x dx

2x 3cos 2y x 15xy 2 dy dx 2x 2ycos 2y x x 3sin 2y x 20y 3 solve as first ordinary differential equations homogeneous clarify the math solving steps

A building contractor s profit in thousands of dollars on each unit in a subdivision is a continuous random variable with probability density function given by f x belov 0 08 8 x if 3 x 8 0 otherwise f x A Find the contractor s expected profit B Find the median profit A The contractor s expected profit is thousand dollars Round to two decimal places as needed

Solve the following compound inequality 7x 8 2x 7 7x 3 Give your answer in interval notation For example if you found 3 x 5 you would enter 3 5 unur answer below

Express the following with rational exponents Select the correct answer below O 2y13 5 O2y5 13 O 2y 3 5 O 2y 5 13 O 2y5 13 O2y 13 5 2 y13

14 Find f t if f t ti t 1 j tek and f 0 i 2j 3k

Solve the following elementary exponential equation AnswerHow 2 Pointe 65x 7 1 36

23 25 4 6 A What is sin A sin A Ente

Evaluate the integral SA csinxdx

15 A particle is moving with the given data Find the position of the particle a t sint 3 cost s 0 0 v 0 2

In Exercises 55 58 express the integral as an infinite series 1 cos t t 55 Jo t sin t dt for all x dt for all x

x 6 y 36 as a polar equation r 0 Enter theta for 0 if needed Question Help Submit Question Message instructor Question 12 0 1 pt 398 i Details Rewrite the Cartesian equation y 3x as a

Score for Question 2 of 6 points 2 Graph the function f x 4 cos x 3 Be sure to clearly label the axes and graph at least one full period of the function Answer

Total score of 14 points Score for Question 1 of 4 points 1 Graph the function f x cot x 6 of the function Answer Be sure to clearly label the axes and graph at least one full period

Consider the curve C given by the portion of the curve a y 4 for y 0 in the ary plane Computea O e 023

Consider a metal plate whose shape is the region in the xy plane bounded by the curves y x y 1 and x 0 Suppose the metal plate has density x y x y Which of the following gives the total mass of the metal plate O VU x y dady O 1 2 y dydz TL x y dyda y dady

5 Let I 2 U 2 and consider the following real valued functions defined on I 1 1 x 2 9 z 24 2 g x 2 x 2 a Show that f does not have a limit as definition 1 1 h x 2 i e Prove the negation of the limit x I b Show that g x and h x have limits as 2 Your work should include a proof that these limits exist and you should find their values

dh 1 6t 3 where t is the time in years and h is the height in centimeters The seedlings are 10 centimeters tall n evergreen nursery usually sells a certain shrub after 9 years of growth and shaping The growth rate during those 9 years is approximated by anted t 0 dt a Find the height after t years h t b How tall are the shrubs when they are sold

Score for Question 3 of 4 points 3 What is the exact value of the trigonometric expression tan sin 2T 3 7x 1 sec State your answer in simplified radical form Answer

Find the general antiderivative of f x C 6x 008 3 3 x2 5

The graph of a limacon curve is given Without using your graphing calculator determine which equation is correct for the graph 5 5 by 5 5 Or 1 3 cos 0 Or 1 3 sin 8 Or 3 sin 0 Or 2 2 sin 0

Evaluate the following determinant 4 1 3 1 34 8 4 4 A Simplify your answer

2 For what values of k is the series a Absolutely convergent b Conditionally convergent c Divergent 710 cos nn n nk 7

Problem 2 Given that tan 0 five trigonometric functions of 0 and sin 0 find the exact value of each of the remaining

Evaluate the determinant XX 2 8 The determinant is Simplify your answer

13 sec 3t tan 3t dt 15 cos 1 5t dt

area la ecuaci n con la figura correspondiente x y 6x 4y 12 2 A C rculo B Elipse 16x2 25y2 64x 100y 236 C Hip rbola 36x2 25y2 144x 50y 781 D Par bola x 10x y 5

Find the integral f x In 3x dx using integration by part

12 Traffic court recorded an average of 45 000 cars dive through the intersection of 50 and Maguire daily with a standard deviation of 540 cars Use the empirical rule to estimate the range where 68 of car totals lie

24 Find the missing leg and hypotenuse 45 3 2

Calculate the following integral using integration by parts We let u X So du 1 and du sec 2 4x da and v and then use the integration by parts formula to find that x sec 4x dx and finally we have a sec 4x dx da da C r sec 42 dr

7 points Calculate the following integral using integration by parts We let u So du a sec x sec 4x dx and then use the integration by parts formula to find that S and du and finally we have da and v x sec 4x dx Noto You can earn partial credit on this problem da dx C x sec 4a da

Evaluate the indefinite integral given below Provide your answer below S dx 9 x 25x 64 dx

4 Let g x x sin 2x a Find g x b Find g T