Definite Integrals Questions and Answers

A volume is described as follows 1 the base is the region bounded by y 2 every cross section perpendicular to the x axis is a semi circle Find the volume of this object volume x 14x 5 and y x 24x 163

10 f f a da 9 2 dz 4 and 19 2 g x dx 5 Compute the following integrals a f x g x dx b f f z 9 f x g x dx c 8 f x 39 x dx f x dx 2 and f x dx 1 help numbers help numbers help numbers

Consider the parametric equations below x 1 et y t 3 t 3 Set up an integral that represents the length of the curve 3 LO 1 Use your calculator to find the length correct to four decimal place dt

The infinitely long region bounded by the graphs of y 0 x 0 and y e 3 is rotated around the x axis The volume of the resulting solid is

1 A cardboard box with a square base is to have a volume of 8000cm a Find the dimensions of the box that will minimize the amount of cardboard to be used 0 1 per cm but the cardboard for the bottom is b The cardboard for box costs thicker so it costs three times as much Find the dimensions that will minimize the cost of the cardboard 7

Find the volume formed by rotating the region enclosed by 3y and y x with y 0 about the y axis

In the following exercises evaluate each integral in terms of an inverse trigonometric function 3 2 391 392 393 394 1 2 395 1 2 S S T 3 dx 1 x 1 3 2 dx 1 x dx 1 x dx 1 x dx x x 1

Let Use these values to evaluate the given definite integrals a S f x 9 x dx b S f x 9 2 dx c S 3 z 3f x 2g x dx f x 2 dz 6 2 dz 14 9 2 dx 3 9 2 dx 7 Find the value a such that a III if af 2 9 2 dx 0

199 18 17 16 15 12 11 18 9 8 6 2 1 1 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Graph of y f x A graph of f x 81 9 2 is shown Using the geometry of the graph evaluate the definite integrals b 3 Stof c f th C f x dx d 18 4f x dx a f x dx f x dx help numbers

64 9 12 1 23 1 A graph of f x is shown The numbers shown represent the geometric area of each Evaluate the following definite integrals f x dx b f f x dx c ff 20 C a f x dx a 2 de d help numbers

119 10 7 6 5 4 3 2 M P of Graph of y f x A graph of f x is shown Using the geometry of the graph evaluate the definite integrals f x dx b 1 a da c f f x dx 4 f 2 dz d e f 6 z dz a help numbers

Find the least squares line for the following data y X 49 67 78 85 91 52743 61 77 87 93 Oy 13 46x 0 04 Oy 1 29x 26 83 Oy 0 74x 23 04 Oy 0 74x 23 04

Convert to liters and add 79 L 863 mL 30 6 L 79 L 863 mL 30 6 L Simplify your answer Type a whole number or a decimal

Every day your heart pumps 7220 quarts of blood through your body How many cup 7220 quarts cups Simplify your answer

Convert the numeral to a numeral in base 10 864 86416

Convert the numeral to a numeral in base ten 1111112 The numeral in base 10 is

Listen 1 9 4x Integrate de sin x c Osin a c Osin a c sin x c

Determine lim x 0 04 3 Oo 3 4 1 0 sin 4x sin 3x

Evaluate O Listen S3 0 1 dx 10 In 2 10 101 5 26 10 101 5 26 Oln 10 V101 In 5 26

Calculate dy dx for 3 x y 6 Vy 3 x O dy da dy da O dy da Ody da 3 y x 3 x y dy 3 9 O da X 3 x Y

Write the Mayan numeral as a Hindu Arabic numeral 10 1 1 2 3 13 14 1 15 16 8 18 19

For the demand equation express the total revenue R as a function of the price p per item q 10p 1000 R P Sketch the graph of the resulting function C No Solution Help 20 90000 80000 70000 60000 60000 40000 30000 20000 10000 20 1000 4 40 60 80 120 140 160 180 200 220 240 260 280 100 120 Ch Fill WebAssign Graphing Tool Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties

Use the graph of H shown to the right to find the limit If necessary state that the limit does not exist lim H x x 0 Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim H x X 0 Type an integer or a simplified fraction OB The limit does not exist B 6 4 2 8 2 2 6

Find area of the region under the curve y 5 x and above the x axis area

The curve C is the graph of y f 1 3t 8 dt Determine x interval s on which the curve is concave upward Cis concave upward on

12 Let 18 to w r dr 2 th w r dr 7 1 8 S Evaluate the expressions below 15 w r dr 2w r 7 dr 12 15 w r dr 4

Let Use the values above to evaluate the integrals listed below S f x g x dx f x g x dx 3 f x 2g x dx Find the value a such that 3 1 z dz 2 1 a dz 12 s 2 de 9 s a dz 12 f x g x dx g x dx a 3 f af af x g x dx 0

At a homeowners association meeting a board member can vote yes vote no or are three motions on which each board member must vote Complete parts a through e below a Determine the number of points in the sample space 27 b Construct tree diagram and determine the sample space Choose the correct tree diagram below O Click here to view tree diagram B Click here to view tree diagram C Click here to view tree diagram A O Click here to view tree diagram D

Jahlil is a golf pro who works at two different golf courses His schedule is to work at Longboat Key golf course for 4 days then work at The Meadows golf course for 3 days and then rest for 2 days He then repeats the cycle If Jahlil is currently on his first day of rest determine what he will be doing a 42 days from today b 109 days from today and c 386 days from today a Jahlil will be b Jahlil will be c Jahlil will be 42 days from today working at The Meadows working at Longboat Key from today from today

3 50 Select the correct choice below and if necessary fill in the answer box to complete your choice OA 3 50 Round to three decimal places OB The solution is not a real number

Complete the square to form a true equation x 2x x x 2x x 2 Simplify your answer Type an integer or a fraction

a Let E and O represent even numbers and odd numbers respectively Complete the table for the operation of multiplication b Determine whether this mathematical system forms a commutative group under the operation of multiplication Explain your answer Complete the table X E O E 0 E E O E Does this mathematical system form a commutative group under the operation of multiplication If not why not Select all that apply A Yes It meets all five requirements needed for a mathematical system to be called a commutative group B No The set of elements is not closed under the operation of multiplication C No The set of elements is not commutative under the operation of multiplication D No There is at least one one element that does not have an inverse under the operation of multiplication E No There is no identity element for the set under the operation of multiplication F No The set of elements is not associative under the operation of multiplication

sin 1 0 a Find all solutions of the equation 1 k An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 8 2mm X 7 5 023 b Find the solutions in the interval 0 2TT 8 A MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

n the following exercises evaluate the definite integra 2 1 2x x 3x 3x x 355 356 1 4 tan x dx dx

A C ch A 2 M Graph of y f x X A graph of f x 9 x 3 is shown Using the geometry of the graph evaluate the definite integrals a b C d 3 f x f x dx numbers 3 6 f x dx 6 f x 6 f x dx 4 f r dr help

TOOTSTTT Graph of y f x A graph of f x is shown Using the geometry of the graph evaluate the definite integrals a b C d e f x dx numbers 2 1 f x dx f x dx 10 So f x 10 f x dx 4f x dx help

Let 2 15 f a dz 13 2 dz 15 9 2 dz 11 g 2 dz 13 5 g x Use these values to evaluate the given definite integrals f x g x da a b x 9 x dx C 3f x 29 x da a 10 3 Find the value a such that af x 9 x dx 0

211 10 9 8 7 6 4 3 2 1 Graph of y f x A graph of f x 10 5x is shown Using the geometry of the graph evaluate the definite integrals a b C d 0 10 5x dx numbers 0 2 10 5x dx 10 5x da dx S 10 10 5x dx help

Find the most general antiderivative of the function f x 6e 3 sec r Use an upper case C for any arbitrary constants F x 4

Determine a region whose area is equal to lim 848 i 1 317 1 3i n

Use the arc length formula to find the length of the curve y 74x 1 x 2 Check your answer by noting that the curve is a line segment and calculating its length by the distance form 370 2 X y 12 10 8 6 4 2 2 X

Given f x 2 and g x 3x 6 Part Part Part Determine fog x Determine go 1 x Are the functions inverses of each other

Set up but do not evaluate an integral for the length of the curve osys112 X 3 sin y 2 3 cos y x dy TO

ind the general indefinite integral Use an upper case C for any arbitrary constants 2 t 2 1 dt

the exact value if any of the following composit

Find the exact length of the curve y In cos x OMXW TU 6

Evaluate the definite integral In 3 0 e 1 e x dx

A pebble is dropped into a calm pond causing ripples in the form of concentric circles The radius r of the outer ripple is increasing at a constant rate of 1 2 ft sec When the radius is 2 3 ft at what rate is the total area A enclosed by the outer ripple changing O O O O a da dt b dA dt c dA dt d dA dt 6 35 5 52 4 60T ft sec ft sec 3 31 F12 sec ft sec

0 0 47 Points DETAILS The graph of a function f is given Let a 1 24 a a Estimate 36 0 1 8 1 b Estimate PREVIOUS ANSWE f f f x dx using four subintervals f x dx using four subintervals

The average value of f x 1 1 x on 0 2 2 is