Definite Integrals Questions and Answers

Evaluate the following indefinite integral 7 dx 7 dx

Calculate the integral x y 8y curves dxdy where D is bounded by the y x 3 x 0

1 Estimate the area under the graph of y 1 from x 2 to x 4 using three approximatin rectangles and RIGHT endpoints Sketch the rectangles

10 Determine whether the integral is convergent or divergent If it is convergent evaluate it 1 2 x 1 3 2 dx In case it s not clear the 3 2 is an exponent on the parentheses

Use series to approximate the value of the integral with an error of magnitude less than 10 5 Use series to approximate the value of the integral with an error of magnitude less than 105 0 4 x c 0 0 4 8 x 0 1 x dx dx Round to five decimal places as needed

The region between the graphs of y x and y 2 and y 2x is rotated around the line x 2 The volume of the resulting solid is

The region between the graphs of y x and y 2x is rotated around the line x 2 The volume of the resulting solid is 13 5m

Estimate the area under the graph of f x rectangles and right endpoints R 1 x 2 Repeat the approximation using left endpoints over the interval 1 2 using four approximatir

Approximate the area under the curve y x from x 3 to x 5 using a Right Endpoint approximation with 4 subdivisions

Determine which values of p make the following integrals converge Give your answer in each case by entering an appropriate inequality sign e g or in the box immediately after p and a numerical value in the second box to define a range of p values for which the integral converges If the integral never converges enter none for the numerical value A 12 P da x ln x P 2 da B P In x P Hint Try the substitution u ln x to start

In the following exercises estimate the areas under the curves by computing the left Riemann sums Lg 42 YA 6 5 4 3 2 1 1 2 3 4 567 8 X

18 R4 for x2 2x 1 on 0 2

1 a Find dV in term of dr What is dV if dr 0 1cm when r 10 cm b Express the radius r in terms of the volume V Find dr in terms of dv Find dr if dV 1 cm when V 36 x cm Ans b r 2 v dr 2 vdv dr 2 36 0 190 2 a Find dS in term of dr What is dS if dr 0 1cm when r 10 cm b Express the radius r in terms of the surface area S Find dr in terms of ds Find dS if dV 1 cm when V 36 cm Ans a dS 8 r dr ds 8 cm 3 a Find volume V in terms of the surface S Find dV in term of ds What is dV if when S 16 cm and that dS 1 cm b Find the surface S in terms of the volume V Find dS in terms of dV Find dS if V 367 cm and that dV cm Ans b S 4x 3 3 2 3 2 3 ds 4m 3 v dv ds 4n 3 36n 1 3 Also be able to explain what each result means

Let L denote the left endpoint sum using n subintervals and let R denote the corresponding right endpoint sum In the following exercises compute the indicated left and right sums for the given functions on the indicated interval 12 L4 for f x on 2 3 x 1

Find the average temperature in the box D x y z 0 x In 4 0 sy In 8 0 z In 16 with a temperature distribution c T x y z 40ex y z The average temperature is Type an exact answer

Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder y x and the planes z 23 y and z 0 The volume of the wedge is www

Evaluate the following integral JSS xy xz yz dV D x y z 3 x 3 6sy 6 5 z 5 xy xz yz dV Simplify your answer

Given the following price demand function find the elasticity of demand E p and determine whether demand is elastic inelastic or has unit elasticity for the following values of p Round your answers two decimal places x 101 400 50p a p 28 E P Determine the demand elastic Inelastic unit elasticity b p 22 E p Determine the demand elastic inelastic Dunit elasticity c p 35 E p Determine the demand elastic inelastic unit elasticity

1 2 The domain is 3 Write the domain in interval notation Write k x log 3x 4

Find the horizontal asymptote of f x Question Help Video X 3x 4 3x3 2x2 1

Question 11 lot yet nswered If f

Use the graph below to fill in the missing values 3 2 1 f 0 4 f 0 0 f x f x 0 x 3 4 f x 0 2 r no 11 1 11 O O

Given P f x where P is the profit in thousand of dollars and is the number of units sold measured in hundreds which of the following is the best interpretation of f 4 19 5 O If the company has a profit of 1 950 they will have sold 4 000 units O If the company has a profit of 19 5 they will have sold 4 units O It will cost 19 500 to make 4 units O If the company has a profit of 4 000 they will have sold 19 5 units O If the company has a profit of 1 950 they will have sold 4 units OIt will cost 19 5 to make 400 units O If the company has a profit of 4 000 they will have sold 1 950 units

1 5 TR Match the function with its graph y 4 x 2 1 D 8543 4 49 OF 24 mations 10 d 23 444 Question Help Video Post to forum 2 1 2 4 O 6543 O 2234 36

1 5 Tranformations The graph below is comprised of transformation of tool kit functions 6 A 5 4 3 7 f x 1 4 3 2 1 Mat 2 3 1 2 Lon 3 Complete a piecewise defined function that describes the graph 4 if x 2 Lin 5 6 q

1 5 Tranformations The solid blue graph below is the original function The red dashed graph is the transformation Select th appropriate movement response and then enter the amount of movement in the answerbox 8 6543 8 6 5 2 3 4 5 6 8 O The graph is shifted right The graph is shifted left O The graph is shifted up The graph is shifted down Question Help Post to forum 3 4 5 6 units units units 8 Q units

4 At time t 1 a particle is located at position x y 1 4 If it moves in the velocity field F x y xy 2 y 8 find its approximate location at time t 1 04 x y 1 05 2 95 1 B Evaluate the line integral where C is the given space curve xyey xyey dy C x 3t y 4t z 4t ostsi 064 415

Consider the differential equation x y 1 dy dx a On the axes provided sketch a slope field for the given diff b Let y g x be the particular solution to the given differe Write an equation for the line tangent to the graph of y g g 1 4 c Find the particular solution y f x to the given differen dy a Hoofd 1 2 1 1 3 C

and the length of the curve corresponding to r t 2t e e over the interval t 1 Note the first component is 2t not 2t

Use the Trapezoidal Rule to approximate the integral using the indicated value of n Write answer as a whole number or reduced fraction 6x dx N 4 33 O 45 2 33 2 16

Use the sum of the first 10 terms to approximate the sum of the series Round your answer to five decimal places 3 cos n n 1 Estimate the error Round your answer to eight decimal places R10 S dx

aphing utility to solve the ed 1 log x 2 1

Sketch the given region of integration R and evaluate the integral over R using polar coordinates 2xy dA R r 0 5 r56 0 50 R CHOEKT

gion in the first quadrant bounded by y 2x 2x y 4 and the y axis is rotate about the lin The volume of the resulting solid is Preview My Answers Sub

Find what value of c does C Sdx 1

The region between the graphs of y x and y 3x is rotated around the line x 3 The volume of the resulting solid is

Find the area of the region between the curves y and y x Area between curves x

Help Lecture 87 Ex 87 2 8 What is the minimum value of t for which a t 5e02 cos 3t damps out to values less th or equal to 1

The table gives the Values of a function obtained from an experiment Use them to estimate 3 6 7 8 9 f x 3 5 2 1 0 5 0 2 0 9 1 3 1 8 X a Estimate R3 4 greater than O one cannot say 4 b Estimate L3 6 4 5 f x dx using three equal subintervals with right endpoints X If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral O less than L f x dx using three equal subintervals with left endpoints X c Estimate M3 0 6 If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than O greater than Oone cannot say L f x dx using three equal subintervals with midpoints x fr f x dx using three equal subintervals with right endpoints left endpoints and midpoints If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than Ogreater than D Pau

2 10 points Construct a polynomial q E P2 R such that 1 P x COS x dx 1 p x q x dx

Use the form of the definition of the integral given in the theorem to evaluate the integral x 4 X 15 4x 8 dx

79 Find 2x dx 93 Select one 3x4 O 2 O O C C C

Graph the point on a polar grid Select one 0

893 EV Select one O O O O 21 8 2t4 C 8t4 C C egral

Help Lecture 92 Lesson 92 and Ex 92 IC 52 For f x x use the definite integral formula to find the exact area under the curve 92 the interval 2 5 Round to 2 d p

1376 Volcanism During an eruption the volcano produced a distinct seismic signature the form s t 4 2cos 3 7t The detector also picked up other seismic anomalies at th same time Which of the following graphs represents s t Select one A B A Blue graph B Green graph C Red graph D Magenta graph y

34 Find the second derivative of g x 3x 2x 11 Select one Og x 90x 120x 22 Og x 54x4 40x 22 90x4 40x 22x g x Og x g x 90x4 40x 22

Cash Supplies Prepaid Insurance Equipment Notes Payable Accounts Payable Unearned Service Revenue Common Stock Retained Earnings Dividends Service Revenue Salaries and Wages Expense Rent Expense 1 2 3 4 5 6 7 Assume the following adjustment data 2 3 4 5 Debit 15 510 Oct 31 2 540 Oct 31 690 Oct 31 4 990 Oct 31 560 4 000 990 29 280 Supplies on hand at October 31 total 530 Expired insurance for the month is 115 Credit Prepare the adjusting entries for the items above List all debit entries before credit entries If no entry is required select No Entry fc account titles and enter O for the amounts Credit account titles are automatically indented when the amount is entened Do not indent manually No Date Account Titles and Explanation Oct 31 4 990 249 1 890 11 300 Depreciation for the month is 70 As of October 31 services worth 830 related to the previously recorded unearned revenue had been performed Services performed but unbilled and no receivable has been recorded at October 31 are 240 Interest expense accrued at October 31 is 90 Accrued salaries at October 31 are 1 505 C 0 8 800 29 280 Debit Credit

pproximate the definite integral using the Trapezoidal Rule and Simpson s Rule with n 4 Compare these results with the approximation of the integral using a graphing utility Round your answers to four ecimal places TT 2 sin x5 dx apezoidal 0 2456 mpson s 0 2456 aphing utility 0 2456 x X

Solve the equation on the interval 0 2x s x 2 0 4 cos What are the solutions in the interval 0 2x Select the correct choice below and if necessary fill in the answer box to complete your choice This question OA The solution set is Type your answer in radians Use integers or fractions for any numbers in the expression Use a comma to separate answers OB There is no solution