Indefinite Integration Questions and Answers

10 p Evaluate the following integrals hint Fubini s Theorem a b 2 4 x cos y dydx x So 0 y 2 ey x dx dy

Use the Table of Integrals in the back of your Cextbook to evaluate the integral 1 81 sec 5t tan 5t 81 tan 5t 81 tan 51 C dt

If g x cos z then g x answer to the nearest hundredth sin 7 and g 5 1 56 x Round your

Evaluate the indefinite integral 1 sin 5x cos 5

28 7 Jo arctan 2x dx Copyright 2021 Cengage Learning All Rights Reservec Copyright 2021 Congngo Leaming All Rights Reserved May not be copied scanned or daplic Editorial review has deemed that any suppressed content does not materially affect the overall leam CHAPTER 7 Techniques of Integration

x arcsin x2 dx entry 87 S 5 tan 0 2 cos 0 S 6 S 4 y4 www 5 t do entry 57 dy entry 26 dt entry 41 7 34 Use the Table of Integrals on the Reference Pages to evaluate the integral 15 arctan t 17 f y 19 fy 6 4y 4y dy 23 coth 1 y S 21 fsin x cos x In sin x dx dy sin 20 cos 0 4 do

41 56 Make a substitution to express the integrand as a rational function and then evaluate the integral 41 f x x 1 42 S 2 x 3 x

First make a substitution and then use integration by parts to evaluate the integral 11 cos x dx

ate the indefinite integral e 4 sin 4x

Use integration by parts to evaluate the integral 2x sin x

a Find the values of p for which the following integral converges Enter your answer in interval notation The integral converges for values of p in the interval For the values of p at which the integral converges evaluato it Integral S x log x dx B

DP Math A x 7 dx using partial fractions x 2 x a Find f

Evaluate SSD x2 y2 dA D x y a2 x2 y2 b2 one where Select

6 Write out the form of the partial fraction decomposition of e function as in Example 7 Do not determine the numerical alues of the coefficients 1 a 2 a 3 a 1 x 3 x 5 x 6 x x 6 x 4 3x 2x b b b 2x 5 x 2 x 2 1 x x4 x x x 2x 1 x 3

5 8 Evaluate the integral using the indicated trigonometric substitution Sketch and label the associated right triangle s fx de dx 1 x x sin 0

How long is the laddes 4 1 far aresin z dz

3 The top of a ladder slides down a vertical wall at a rate of 0 75 m sec At the moment when the bottom of the ladder is 15 meters from the wall it slides away from the wall at a rate of 04 m sec How long is the ladder

Solve the system dx dt 2 1 14 5 2 2 B with a 0 3 x Give your solution in real form 1 x2 An ellipse with clockwise orientation 1 Describe the

Determine whether the quantities in the table re If yes give the constant rate 11 Times at Bat Hits 6 4 10 8 15 12 20 15 Proportional Rate

oblem 1 Let v 6 1 0 1 v2 0 1 6 1 and b 1 8 1 4 Let II be the subspace or R spanned by and v Find projgb using the Euclidean inner product Enter your answer symbolically Enter the four components

6 Use double integrals to find the volume of the given solid The solid below e and above z that intersects the ry plane in the region R r y 0 y 1 0 x y R

propriate Determine the metric unit tha

43 a 0 o b 0 25 x2 V25 1 25 x 25 x dx 25 x sin sin sin 3 in 3 c 3 c

1 fxe dx u x dv e x dx 2 f x In xdx u ln x dv x dx 3 fx cos 4x dx u x dv cos 4x dx 4 f sin x dx u sin x du dx 5 42 Evaluate the integral 5 Ste dt 6 Sye dy 11 f x 2x cos x dx 13 f cos x dx 15 ft In t dt 17 f t csc t dt 19 f In x dx 21 fear fe x cos x dx

5 42 5 Evaluate the integral te di

D Question 3 Determine the equations of the vertical a function f x f x 2

0 Continuity a State the definition of a function f being continuous at an x value a Note Give the mathematical definition not an explanation of holes and gaps b Draw a picture of each of the three types of discontinuities removable jump and infinite Be sure to label each picture with the type of discontinuity

Find the area of the triangle below Round you answer to 1 decimal place B A 113 33 7 ft

4 3 26 6 36 5 C 40 25 cm 70 Diagram not drawn to scale C D 11 2 17 1

X x 20y 4 5y 2y 1 The solution y satisfies the equation a ay by e for some constants a b c and d Find these b C d y 1 1 x 1 cx d y 1 0 I

Determine which integration strategy will work the best for each integral 4x 2 x 10x 34 J r sec r tan x dx cos r sin r dr S I x dr x 2x 1 x 10x 2 x 4x 2 4x r 10r dx da dx da a Integration By Parts b Split into two integrals Use Substition and Inverse Trig Function c Partial Fraction Decomposition d Trigonometric Substitution e Long Division then Partial Fraction Decomposition

1 22 4 52 x2 4x 5 A B D arctan z 2 C arcsin x 2 C In x 4x 5 C 2 22 52 C 12

An antiderivative for A B C D E 1 21 2 x 2x 2 In In x 2x 2 is arcsec x 1 arctan x 1

5 12 points Evaluate the following indefinite integral e sin dr

set with 2 elements Z f g let Z1 Z Z2 ZX Z nEN Zn Zn 1 x Z How many elements does Zn have prove by induction

Show that the curve defined by a vector valued function r t t t cos t t sin t lies on the 2 z cone x y 4 Sketch the cone and the curve

a b of 27 x 2 3 dx La x 9 2 3 dx 1 x 9 C S 10 0 dx

At the beginning of an experiment a scientist has 172 grams of radioactive goo After 255 minutes her sample has decayed to 2 6875 grams What is the half life of the goo in minutes Round to one decimal place The half life of the goo is Find a formula for G t the amount of goo remaining at time t G t How many grams of goo will remain after 68 minutes Round to one decimal places There will be grams of goo after 68 minutes

The half life of Radium 226 is 1590 y O after 1000 years mg years If a sample contains 400 mg how many mg will remain

11x Use the unit circle to find the value of cos and even 6 or odd trigonometric functions to find the value of cos 05 11 6 4 1 0 0 1 0 1 16 1 0 4 3 Q 5 Select the correct choice below and fill in any answer boxes within your choice O A 11x 6 Type an exact answer using radicals as needed Simplify your answer Rationalize the denominator OB The expression is undefined cos

Find the length of the arc s on a circle of radius r intercepted by a central angle 0 Express the arc length in terms of Then round your answer to two decimal places Radius r 19 inches Central angle 0 5 S 19 inches 36 Simplify your answer Type your answer in terms of Use integers or fractions for any numbers in the expression S inches Type your answer rounded to two decimal places

17 Choose the figure that shows an angle of 6 lies Choose the correct answer below A B radians in standard position then state in which quadrant the angle C D Q

Graph the solution set of the inequality w 5x15

Graph the solution set of the inequality where x 7x 2251

Which two expressions are prime polynom x 2 5x 3 x 4 xy 3 x 2 7x 6 2xy 4x 2 y 3 5x 3 8y 2 x 4 y 3 3x 3 4x 2 y 2 x

P roll 1 36 3 2 36 3 36 543 6 5 36 7 8 761 36 853 36 9 4 36 10 3 36 11 2 36 12 1 36 Each person takes turns rolling two dice If the sum is odd the person playing odds gets points equal to the sum of roll If the sum is even the person playing evens gets points equal to the sum of the roll Note that the points earned independent of who is rolling the dice If Jessica is challenged to a game of Sums which statement below is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens O E evens will be more because there are more even numbers that result from rolling two dice Therefore Jessica should play evens O E odds will be more because the probability for each odd number being rolled is greater Therefore Jessica should play odds OE evens will be more because the value of the even numbers on the dice are more Therefore Jessica should play evens Flovone Flodde herauco the different prohabilities and values and un halancinn out creating a fair name

As a project for math class two students devised a game in which 3 black marbles and 2 red marbles are put into a bag First the players must decide who is playing black marbles and who is playing red marbles Then each player takes a turn at drawing a marble noting the color replacing the marble in the bag and then drawing a second marble and noting the color before returning it to the bag The point scheme for the game is detailed in the table below Point Values for Marble Game Black Marble Points Both black 2 points Different colors 1 point Both red 0 points Red Marble Points Both red 4 points Different colors 1 point Both black 0 points If Seth is challenged to a game by a classmate which statement below is correct in all aspects in helping him make the correct choice Since E black 0 24 and E red 0 16 Seth should choose to play black marbles E red will be twice that of E black so Seth should choose to play red marbles Since E red E black it is a fair game so it doesn t matter which color Seth chooses

A manager records the number of hours X each employee works on his or her shift and develops the probabi distribution below Fifty people work for the manager How many people work 4 hours per shift Probability Distribution Hours Worked X O 0 3 4 5 6 7 8 Probability P X 0 1 0 14 0 3 0 36 0 06

Sonia rolls a six sided number cube 12 times and records if she rolls a 2 What is the number of trials for this binom experiment 0000 2629 02 6 12 18

Find the solution of the following pure convection problem PDE IC U 2 8 0 t ur 0