Question: Set up an integral for the volume
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
(a) About the x-axis
(b) About y = 1
Transcribed Image Text:
у — 0, у — сos?х, —п/2 <х<п /2 TT
> What are the advantages and disadvantages of an OODBMS?
> Name and describe the 13 mandatory features of an OODBMS.
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> You read in this appendix that: An examination of the UCL's Inventory Management module reporting requirements uncovered the following problems: • The Inventory module generates three reports, once of which is an Inventory Movement Report. But the inven
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> During peak periods, Temporary Employment Corporation (TEC) places temporary workers in companies. TEC’s manager gives you the following description of the business: • TEC has a file of candidates who are willing to work. • If the candidate has worked be
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> What steps must be completed before the database design is fully implemented? (Make sure that you list the steps in the correct sequence and discuss each step briefly.)
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> What is a module, and what role does a module play within the system?
> Write the connectivity and cardinality for each of the entities shown in Question 4. Details from Question 4: PART PART VEND VENDOR PK PART CODE PK,FK1 VEND ID PK,FK2 PART CODE PK VEND ID PART PROD PK,FK1 PART CODE PK,FK2 PROD CODE PROD_CUST PRODUCT
> What is a partial dependency? With what normal form is it associated?
> The dependency diagram in Figure Q6.8 indicates that a patient can receive many prescriptions for one or more medicines over time. Based on the dependency diagram, create a database whose tables are in at least 2NF, showing the dependency diagram for ea
> The dependency diagram in Figure Q6.7 indicates that authors are paid royalties for each book that they write for a publisher. The amount of the royalty can vary by author, by book, and by edition of the book. Figure Q6.7 Book royalty dependency diagr
> The administrators of Tiny College are so pleased with your design and implementation of their student registration/tracking system that they want you to expand the design to include the database for their motor vehicle pool. A brief description of opera
> Given the dependency diagram shown in Figure Q6.6, answer items 6a-6c: FIGURE Q5.6 Dependency Diagram for Question 6 a. Identify and discuss each of the indicated dependencies. b. Create a database whose tables are at least in 2NF, showing the depen
> When is a table in BCNF?
> When is a table in 3NF?
> When is a table in 2NF?
> When is a table in 1NF?
> Suppose that someone tells you that an attribute that is part of a composite primary key is also a candidate key. How would you respond to that statement?
> How would you describe a condition in which one attribute is dependent on another attribute when neither attribute is part of the primary key?
> Why is a table whose primary key consists of a single attribute automatically in 2NF when it is in 1NF?
> What is a surrogate key, and when should you use one?
> Define and discuss the concept of transitive dependency.
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> What actions are taken during the database initial study, and why are those actions important to the database designer?
> Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. (a)
> Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. (a)
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) Rz about BC
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) Rz about AB
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) Rz about OC
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R3 about OA
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R2 about BC
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R2 about AB
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R2 about OC
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. у 3 sin x, у—2х/п, х>0 y
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R2 about OA
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R1 about BC
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R, about AB
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) R1 about OC
> Refer to the figure and find the volume generated by rotating the given region about the specified line. C(0, 1)| R2 B(1, 1) y= Vx A(1, 0) Rj about OA
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у — х, у — 0, х — 2, х — 4; about x
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. x = y', x = 1 – y²; about x = 3
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. ху— 1, у — 0, х — 1, х— 2;B about x -
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у —х', у — 0, х — 1; about x
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = sin x, y = cos x, 0 < x </4; about y = -1
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. у — 1/х, у — 1/х, х—2 y
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = 1 + sec x, y = 3; about y = 1
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у — х", у — 1, х — 2;B about y — -3 |3D
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у —х, х — у?;B аbout y — 1
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. х — 2 — у?, х —у%;B about the y-aхis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y² = x, x = 2y; about the y-axis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = 6 – x², y = 2; about the x-axis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = x', y = x, x> 0; about the x-axis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. 2х — у?, х — 0, у — 4;B about the y-ахis
> Suppose that a region / has area A and lies above the x-axis. When / is rotated about the x-axis, it sweeps out a solid with volume V1. When / is rotated about the line y = -k (where k is a positive number), it sweeps out a solid with volume V2. Express
> Some of the pioneers of calculus, such as Kepler and Newton, were inspired by the problem of finding the volumes of wine barrels. (In fact Kepler published a book Stereometria doliorum in 1615 devoted to methods for finding the volumes of barrels.) They
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. у — х3 — 4х, у %3 2х y
> A hole of radius r is bored through the center of a sphere of radius R > r. Find the volume of the remaining portion of the sphere.
> A hole of radius r is bored through the middle of a cylinder of radius R < r at right angles to the axis of the cylinder. Set up, but do not evaluate, an integral for the volume cut out.
> A bowl is shaped like a hemisphere with diameter 30 cm. A heavy ball with diameter 10 cm is placed in the bowl and water is poured into the bowl to a depth of h centimeters. Find the volume of water in the bowl.
> Find the volume common to two spheres, each with radius r, if the center of each sphere lies on the surface of the other sphere.
> Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles.
> (a) Cavalieri’s Principle states that if a family of parallel planes gives equal cross-sectional areas for two solidsS1 and S2, then the volumes of S1 and S2 are equal. Prove this principle. (b) Use Cavalieri’s Princip
> Solve Example 9 taking cross-sections to be parallel to the line of intersection of the two planes.
> (a) Set up an integral for the volume of a solid torus (the donut-shaped solid shown in the figure) with radii r and R. (b) By interpreting the integral as an area, find the volume of the torus. R-
> The base of S is a circular disk with radius r. Parallel cross sections perpendicular to the base are isosceles triangles with height h and unequal side in the base. (a) Set up an integral for the volume of S. (b) By interpreting the integral as an area,
> For what values of m do the line y = mx and the curve / enclose a region? Find the area of the region.
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. у 3 (х — 2), у %3Dх 2)°, y = y =
> Suppose that /. For what value of c is the area of the region enclosed by the curves y = cos x, / equal to the area of the region enclosed by the curves /
> Find the values of c such that the area of the region bounded by the parabolas /
> (a) Find the number a such that the line x − a bisects the area under the curve / (b) Find the number b such that the line y = b bisects the area in part (a).
> Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal area.
> Find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at (1, 1), and the x-axis.
> The curve with equation / is called Tschirnhausen’s cubic. If you graph this curve you will see that part of the curve forms a loop. Find the area enclosed by the loop.
> The figure shows graphs of the marginal revenue function R9 and the marginal cost function C9 for a manufacturer. [Recall from Section 4.7 that R(x) and C(x) represent the revenue and cost when x units are manufactured. Assume that R and C are measured i
> Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their velocity functions. (a) Which car is ahead after one minute? Explain. (b) What is the meaning of the area of the shaded region? (c) Which car is ahead af
> The rates at which rain fell, in inches per hour, in two different locations t hours after the start of a storm are given by / and / Compute the area between the graphs for / and interpret your result in this context.
