Definite Integrals Questions and Answers

20 p 3 Determine whether the function f x x for rational x in 0 1 lo for irrational x in 0 1

1 Let h x t 1dt for 1 x 1 a Find h 1 b Find h 1

Copy vectors u v and whead to tail as needed to sketch the indicated vectors a u v b u vw C U V d u w Choose the correct sketch for uv OA OB odo OC OD

F dr Use Stokes Theorem and Theorem 10 in section 16 7 to find Sc x y z 2y xz x y C is oriented counterclockwise as viewed from above and is th ntersection of the plane z y 2 and the cylinder x y 1 F ds p g 0 Blas

3 x 8 y ve x y 8 egrileri taraf ndan s n rlanan b lgenin alan n hesaplay n z 25 puan

Sketch the coordinate axes and then include the vectors u v and uxv as vectors starting from the origin u 8i v 2j Which of the following graphs contains u v and u xv O A O C u uxv y UXY OB OD uxy t uxy X

Without graphing describe the shape of the graph of the function Find the second coordinates of the points with first coordinates 0 and 1 f x e 1 3x The graph exponentially decays Find the second coordinates of the given first coordinates f x e 1 3x f 0 1 f 1 Round to one decimal place as needed x 0

For what real values of the constant k does the region lying under the curve y 1 above the z axis and to the right of the line have infinite area but gives rise to a solid with finite volume when rotated about the x axis Ik H 1

Approximating the Area of a Plane Region In Exercises 1 6 use the rectangles to approximate the area of the region Compare your result with the exact area obtained using a definite integral See Example 1 1 f x 2x 3 0 1 2 f x 1 5 0 5 1 2 3 4 5 5 Usi Mid regie inter 7

Using the Midpoint Rule In Exercises 13 18 use the Midpoint Rule with n 4 to approximate the area of the region bounded by the graph of f and the x axis over the interval Sketch the region See Examples 2 and 3 Function 13 f x 2x Interval 1 3

How many subsets of cardinality 5 does a set with 12 elements have

Determine if the improper integral is convergent or divergent and calculate its value if it is convergent 0 Te 0 7x 7e dx Calculate the value of the improper integral Select the correct choice below and if necessary fill in the answer box to complete your choice 00 O A 7e 7x dx 0

1 What should be for the path independent of 2 4 xy y A Y dx 2xy x y dy 1 2 Moreover evaluate the integral for this value of X Answer

Consider the box C 0 x 2 0 y 1 0 1 Calculate the flux integral fevnds where n is outward normal vector and v x y z 7x 287 y e xz sin e

Calculate the number of possibilities From a standard deck of 52 cards in how many ways can 7 cards be selected

4202 B 2 0 2 8 5 Find the volume of the solid bounded below by the plane z 6 and above by the sphere a y 2 7 2 62 62 460 Write your answer as a reduced fraction Volume x not a valid fraction 3

Use power series to solve the differential equation x 3 y 2y O

xy x 1 x sin x y dA R 0 6 0 3 R JR dA R 0 1 x 3 3 ye xy dA R 0 2 0 3 X

Evaluate each of the following a 97 b A i 5 n lim 3

jate x In x f x dx using the substitution u In f x Assume f 0 8 and f 1 9 Type your answer completely and include the

Assume that x ff 1 dt F 1 It f 1 dt 26 and F 1 13 what is F 8 and why Explain your answer is detail and type it in the space provided If

Integrate F y sin z i x sin z j xy cos z k around the circle cut from the sphere x y z 5 by the plane z 1 clockwise as viewed from above

Find lu x vl ux v v 4 60 u 3 Determine whether u x v is directed into the screen or out of the scree Oux vis directed into the screen Oux v is directed out of the screen

A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R where Chemical P costs 500 a unit and chemical R costs 3 500 a unit The company wants to produce as many units of chemical Z as possible with a total budget of 280 000 z 60p 75 0 25 A How many units each chemical P and R should be purchased to maximize production of chemical Z subject to the budgetary constraint Units of chemical P p Units of chemical R r B What is the maximum number of units of chemical Z under the given budgetary conditions Round your answer to the nearest whole unit Max production

A company manufactures 2 models of MP3 players Let x represent the number in millions of the first model made and let y represent the number in millions of the second model made The company s revenue can be modeled by the equation R x y 120x 50y 4x 3y xy Find the marginal revenue equations R x y 120 2 4x y 08 Ry x y 50 3 2 y x We can acheive maximum revenue when both partial derivatives are equal to zero Set R 0 and Ry 0 and solve as a system of equations to the find the production levels that will maximize revenue Revenue will be maximized when X OF

For the function f x x ln 1 x 3x 2tan x determine intervals of increase and decrease local maximum and minimum values intervals of concavity and inflection p not just write the answers show how you found your answers Write your solution on paper and upload a PDF or image of your solution Attach File

Finding Mean Variance and Standard Deviation In Exercises 1 12 use the given probability density function over the indicated interval to find the a mean b variance and c standard deviation of the random variable d Then sketch the graph of the density function and locate the mean on the graph See Examples 1 2 and 3 1 f x 3 0 3 2 f x 1 0 4 3 f t 4 f x 18 x 0 6 0 4 4 5 f x 42 1 4 6 f x 2x 2 0 1 7 f x 1x 0 2 8 f x x 0 4 9 f x 6x 1x 0 1 10 f x x 4 x 0 4 11 f x 4 x 0 4 12 f x 9 x 0 9 18

Question Determine the interval s for which the function shown below is increasing

f x S dx using the substitution u 1 f x Assume that f 0 0 and f 1 6 Type your complete solution in the space provided 0 1 f x 2 For the toolbar press ALT F10 PC or ALT FN F10 Mac Evaluate

Find the volume of a right pyramid that has a square base in the xy plane 1 x 1 1 y 1 an the vertex at 0 0 1 The figure below shows a pyramid with the vertex at 0 0 3 Your problem will value for the vertex Round your answer to four decimal places have a different Pyramid N 0 5 0 X 0 5 1050 05 1 y

Function fis defined as f x cos 2x sin 3x 5 Using the subintervals of 0 1 6 1 31 and 3 6 find the trapezoidal approximation of o A B 33 427 27 355 f x dx

Solve the following compound inequality x 3 4x 15 2x 13 Submit your answer by dragging the movable blue points on the number line For an interval that extends to or 00 move the blue points to the right or left end of the number line shown as a dashed line You can select whether each endpoint of your chosen interval is open or closed by sliding the respective orange switches up or down Note that the blue line segment above the number line indicates the interval you have chosen and whether the endpoints are open or closed Note The orange coordinates shift vertically and the blue coordinates shift horizontally Provide your answer below

Find the Fourier Cosine Series of f x x 2x on the interval 0 3

Express the following in radical form Select the correct answer below O O O O 1 Fy 1 ys

6 x 7x 12 by x 4 7 2x x 36 by x 4 8 9x 3x 20 by 3x 5 9 10x 39x 14 by 2x 7 10 8x 10x 63 by 2x 7

The following formula gives the area A of a trapezoid with base lengths b and b2 and height h 1 A b b b h 2 Find the area of a trapezoid with base lengths 3 and 7 and a height of 8 Provide your answer below

Calculate the integral if it converges If it diverges enter diverges for your answe dx e5z 1 e z

Determine the variables in the expression below Enter your answer as a list separated by commas 3r 6hr 4h

Evaluate the integral If the integral converges determine the number it converges to If the integral diverges enter divergent 1 In 8x dx 8

Find the area under the curve y 9 area 3xe for x 0

ind the center of mass of a thin plate covering the region between the x axis and 20 me curve y 4 x 8 if the plate s density at a point x y is 8 x 2x X The center of mass is x y Type an ordered pair Type integers or simplified fractions

3 Find the Riemann sum for f x sinx 0 x n with n 4 taking the sample points to be left endpoints Sketch the graph and the rectangles 1 88

Find the arc length of the polar curve described by r 10 10 cos 0

Find the area of the region outside r 7 7 sin 0 but inside r 21 sin 0

Find the area of the region which is inside the polar curve r 4 cos 0 and outside the curve r 3 2 cos 0 The area is

Find the area enclosed by the line y 2x and the parabola y 2 x 4x X

A tank has the shape of an inverted circular cone with base radius 6 m and height 12 m It s filled with water to a height of 10 m Find the work required to empty the tank by pumping all of the water to the top of the tank The water mass density is 1000 kg m

a Rectangular equation b Identify the shape if possible The shape is a n Select an answer Question Help Video Message instructor 0 Submit Question Question 10 0 1 pt 398 i Details Convert each equation from Polar to Rectangular Identify the shape if possible 5TT 4

Complete the function table X 3 1 3 4 X f x 0 0 0 0

A line passes through the point 6 1 and has a slope of 1 Write an equation in point slope form for this line 00 64