Indefinite Integration Questions and Answers

Find the slope of the graph of the function at the given point Use the derivative feature of a graphing utility to confirm your results Function Point 0 0 f 0 8 sin 0 0 f 0

Evaluate the following integral Ax dx

Find the following integral Note that you can check your answer by differentiation S 6e4 3 3 dy

b 0 75 m B Z 3 m 1 of 1 1 5 m y Determine the angle between cables AB and AC Suppose that a 1 8 m and b 1 2 m Eigure 1 Express your answer using three significant figures 0 Submit VASO It vec Request Answer Return to Assignment Provide Feedback www

5 Find the centerold of the region bounded by the graphs of Y X and X Y 6 X T 4

23 Bearing A boat travels on a course of bearing N 37 W for 79 5 miles How many miles north and how many miles west has the boat traveled

Evaluate the indefinite integral

Evaluate the indefinite integral S 11

Evaluate the indefinite integral

Consider the graph shown Check all that apply a f 2 exists lim f x exists 112 None of the above

Let R be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y 1 x 1 OB OA JO X 18 y 1 revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice S dx dx Type exact answers I dx Type exact answers

Given lim f x 8 and lim g x 4 evaluate x 3 x 3 lim g x ln 6f x 5 x 3 lim 69 2 e f a lim 6f x 5g x x 3 lim x 3 cos f x g x

1 point Evaluate the integral 1 2 1 6 5 csc t cot t dt

1 point Evaluate the integral dt cos 71 1 tan 7t

1 For 0 0 2 name all the angles on the unit circle where cos 0 What do you notice about these angles

Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very nearly linear A cricket produces 113 chirps per minute at 70 F and 163 chirps per minute at 80 F a Find a linear equation that models the temperature 7 as a function of the number of chirps per minute N T X b What is the slope of the graph What does it represent The slope means that the temperature in Fahrenheit degrees increases X as rapidly as the number of cricket chirps per minute c If the crickets are chirping at 160 chirps per minute estimate the temperature Round your answer to the nearest whole number OF

The surface area A of a right circular cylinder is given by the formula A 2xrh 2xr2 where r is the radius and his height Find the height of a right circular cylinder whose surface area is 80x square centimeters and whose radius in centimeters What is the height of the cylinder cm

On summer days on Mars close to its equator the temperature can be around 55 Celsius What is this temperature in degree Fahrenheit 55 C F It

Use Simpson s rule with n 10 to approximate cos x 1 5 83 dx

8 4 pts The rational function g x asymptote 2x 3x 5 x 1 2x 3x s X 1 has an oblique asymptote Find the equation of its oblique 4X 8X 1x 4x 8x IX

24 Let f x 2 2x 11 Show that there is no value c in 0 3 such that f 3 f 0 f c 3 0 Explain why this does not contradict the Mean Value Theorem

Use the figure below which shows the graph of y f x to answer the following questions 1 0 A Between x 3 and x 3 B Between x 3 and x 0 Click on the graph to ge A Estimate the integral f f x dx You will certainly want to use an enlarged version of the graph to obtain your estimate B Which of the following average values of f is larger 4 X

5 3 Points DETAILS SCALCET9 2 XP 8 004 Trace or copy the graph of the given function f Assume that the axes have equal scales Use estimates of the derivative of f to sketch the graph of f on the same coordinate axes y O Q 20 DO

Identify the number of chiral centers present in Vitamin D3 shown below HO 4 2 3 Vitamin D3

CURRENT OBJECTIVE Use substitution to find an indefinite integral with the power rule Question Find the following antiderivative 7x 3x 2 dx Do not include the constant C your answer For example if you found the antiderivative was 2x C you would enter 2x

Find the volume of the solid generated when R shaded region is revolved about the given line x 4 2 secy x 4 y T 3 and y 0 about x 4

Question A particle travels according to the velocity function v t 4t 10 m sec What is the total distance traveled by the particle over the time interval 2 12 Enter your answer as an exact fraction if necessary and do not include units in your answer

Calculate the derivative ftant sin x dx 0 dt J1

Find a function f and a positive number a such that f x 12x a 1 2 f t 2 160 dt 62 6x 2 t6

Evaluate x 0 csc x dx Include the constant C in your answer Provide your answer below

Evaluate I cos cos 3x sin 3x dx Include the constant C in your answer Provide your answer below

1 point Find the derivative of the function g r x 16 dx g r

1 point Evaluate the integral S 1 3 du 9 1 u 3 u

Find the area of the region described The region between the line y x and the curve y 2x 25 x in the first quadrant The total area of the shaded region is Type an exact answer

Evaluate du Pr u 16 u

Question Determine the following indefinite integral 111 Do not include C in your answer For example if you found the antiderivative was 2t C you would enter 2t 11t7cos t dt

The average annual pay for truckers P in a certain country in thousands of dollars can be approximated by the following function where x represents the number of years since 200 P 0 399x 7 12x 79 4 5 x 15 Find the average annual pay in 2009 Write the expression that can be used to find the average annual pay in 2009 Do not simplify

Shmon factor in the given 7 4y 1 2 3 4y 1 7 4y 1 2 3 4y 1 3 0 Factor completely

Using the substitution usin 2 25 S where the constants K 25 x dx we obtain m K sin u cos udu m r 25 r dx C and n 0 Using this result and your knowledge about indefinite integrals of powers of sin u and cos u find the indefinite integ 2 Note Your answer should be in terms of x not u

T In the following exercises set up a table of values and round to eight significant digits Based on the table of values make a guess about what the limit is Then use a calculator to graph the function and determine the limit Was the conjecture correct If not why does the method of tables fail 44 limsin 7 0 0 e 0 1 0 01 0 001 0 0001 sin 7 a b C d 8 0 1 0 01 0 001 0 0001 sin 7 e f g P

Find the area of the shaded region shown in the graph CE 20 y 20 sin x y 20 cos x R 2 O

Find the indefinite integral x 362 x 49 dx 0 0 C

Evaluate the indefinite integral 7 dx

Sketch the angle in standard position and draw an arrow representing the correct amount of rotation Find the measure of two other angles one positive and one negative that are coterminal with the given angle and closer to the given angle than any other coterminal angle Give the quadrant of the angle if applicable A 62 Choose the correct graph below where the curve on each graph traces the angle beginning at the positive x axis and ending at the ray O A Ay 0 62 5 OB Ay Q O C

6 Fill in each blank with the radian measure of the angle on the unit circle

Evaluate the indefinite integral 32 62 2 52 5 dz 32 3

Find the position and velocity of an object moving along a straight line with the given acceleration initial velocity and initial position a t 64 v 0 50 and s 0 10 v t 64t 50 s t

For the following exercises for each pair of functions find a f g x and b g f x Simplify the results Find the domain of each of the results 42 f x 3x g x x 5 43 f x x 4 g x 4x 1 44 f x 2x 4 g x x 2 45 f x x 7 g x x 3 46 f x x g x x 9 3 47 f x 2 8 x 2x 12 48 f x x 11 g x x x 4

2 5 pts Prove 1 of the following identities for all permissible values of the variable Clearly YAMA AT indicate which identity the selected identity and the chosen side State any non permissible values A 1 sin x cos x cos x tan x tan x 1 B sinx cosx cos x sinx cosx secx csc x sinx 3 Solve the following equation for in the units specified Give the general form and solve for the specified domain Give exact solutions State any non permissible values 2 sin 0 tan 0 cos 0 1 0 F 3

Evaluate the indefinite integral s 2 42 2 2 da