# Definite Integrals Questions and Answers

Calculus

Definite IntegralsGiven the graph of y f x shown as a red dashed curve drag the green movable points to draw the graph Notice that you can control the positioning of the reflective function with the coordinate labeled Drag Function and contra the width of the reflection with the coordinate labeled Control Width Because the green curve starts in the same position as the red dashed curve you may need to drag the green curve away from its initial position in order to see the red dashed curve Provide your answer below 10 Drag Function 5 10 Control dth 0 5 10

Calculus

Definite IntegralsA 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

Calculus

Definite IntegralsA 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

Calculus

Definite IntegralsFor 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

Calculus

Definite IntegralsFinding 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

Calculus

Definite IntegralsQuestion Determine the interval s for which the function shown below is increasing

Calculus

Definite Integralsf 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

Calculus

Definite IntegralsFind 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

Calculus

Definite IntegralsA function assigns to a bit string the number of one bits in the string Find the domain and range of the function Domain is Range is

Calculus

Definite IntegralsFind the slope of the graph of the function at the given point Use the derivative feature of a graphing utility to confirm your resu Function g t 8 cos t 4 g 8sin t Point 12 X Your answer cannot be understood or graded More Information

Calculus

Definite IntegralsFunction 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

Calculus

Definite IntegralsSolve 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

Calculus

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

Calculus

Definite Integrals6 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