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Write the integral that gives the surface area generated when the curve is revolved about the x-axis. Do not simplify.y = ln x4  on [1, ]

Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at  and . The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola  to the parabola .

“The authors and promoters of this desperate conspiracy have…meant only to amuse, by vague expressions of attachment to the parent state, and the strongest protestations of loyalty to me, whilst they were preparing for a general revolt… The resolutions of Parliament breathed a spirit of moderation and forbearance; conciliatory propositions accompanied the measures taken to enforce authority… I have acted with the same temper, anxious to prevent, if it had been possible…the calamities which are inseparable from a state of war; still hoping that my people in America would have discerned the traitorous views of their leaders, and have been convinced, that to be a subject of Great Britain, with all its consequences, is to be the freest member of any civil society in the known world.”-King George III, Speech to Parliament, October 27, 1775Based on the excerpt, which of the following best describes King George’s view of the colonists?

“We hold…that on their separation from the Crown of Great Britain, the several colonies became free and independent States, each enjoying the separate and independent right of self-government; and that no authority can be exercised over them…but by their consent… It is equally true, that the States…that the government created by it is a joint agency of the States, appointed to execute the powers enumerated and granted by that instrument; that all its acts not intentionally authorized are of themselves essentially null and void, and that the States have the right… to pronounce, in the last resort, authoritative judgement on the usurpations of the Federal Government… Such we deem to be inherent rights of the States.”-John C. Calhoun, statement adopted by a convention in South Carolina, 1832As described in the excerpt, which individual or body makes the final decision on whether a law is valid in a state?

“Gov. Randolph observed that the confederation is incompetent to any one object for which it was instituted.  The framers of it wise and great men; but human rights were the chief knowledge of the times when it was framed so far as they applied to oppose Great Britain.  Requisitions for men and money had never offered their form to our assemblies.  None of those vices that have since discovered themselves were apprehended.”-Dr. James McHenryWhy was maintaining state power and preventing abuses by the national government a major concern for many Americans in the 18th century?

“We might feel a pride in the reflection, that our young country…was the first to adopt with any efficacy, the penitentiary system of prison discipline, and the first to attempt to prevent the commission of crimes, by seeking out the youthful and unprotected, who were in the way of temptation, and by religions and moral instruction, by imparting to them useful knowledge, and by giving them industrious and orderly habits, rescuing them from vice, and rendering them valuable members of society… To confine these youthful criminals…where no, or scarcely any, distinction can be made between the young and the old, or between the more or less vicious, where little can be learned but the ways of the wicked, and from whence they must be sent to encounter new wants, new temptation, and to commit new crimes, is to pursue a course, as little reconcilable with justice as humanity; yet, till the House of Refuge was established there was no alternative.”-Society for the Reformation of Juvenile Delinquents in the City of New York, Fourth Annual Report, 1829The above account best reflects what growing reform sentiment during the period 1820 to 1848?

“If, then education be of admitted importance to the people, under all forms of government, and of unquestioned necessity when they govern themselves, it follows, of course, that its cultivation and diffusion is a matter of public concern and a duty which every government owes to its people… “Many complain of this tax, not so much on account of its amount as because it is for the benefit of others and not themselves.  This is a mistake; it is for their own benefit, inasmuch as it perpetuates the government… “He who would oppose it, either through inability to comprehend the advantages of general education, or from unwillingness to bestow them on all his fellow citizens, even to the lowest and poorest, or from dread of popular vengeance, seems to me to want either the head of the philosopher, the heart of the philanthropist, or the nerve of a hero.”-Representative Thaddeus Stevens, Speech to the Pennsylvania Legislature, 1835The first free public education system in the United States began in which of the following colonies?

“Of all the dangers and misfortunes which could befall this nation, I should regard that of its becoming a warlike and conquering power, the most direful and fatal… This is no war of defense, but one unnecessary and of offensive aggression.  It is Mexico that is defending her fire-sides, her castles and her altars, not we.”- Henry ClayBased on the above quote, how did the Mexican War cause a high level of controversy in the United States?

“However, it matters very little now what the king of England either says or does; he hath wickedly broken through every moral and human obligation, trampled nature and conscience beneath his feet, and by a steady and constitutional spirit of insolence and cruelty procured for himself an universal hatred.  It is now the interest of America to provide for herself.  She hath already a large and young family, whom it is more her duty to take care of, than to be granting away her property to support a power who is become a reproach to the names of men and Christians…if ye wish to preserve your native country uncontaminated by European corruption, yet must in secret wish a separation.”Thomas Paine, Common Sense, 1776Which of the following best explains the impact of publications like the one excerpted here?

“Another sign of our times, also marked by an analogous political movement, is the new importance given to the single person… “The scholar is that man who must take up into himself all the ability of the time, all the contributions of the past, all the hopes of the future.  He must be a university of knowledges… The world is nothing, the man is all; in yourself is the law of all nature, and you know not yet how a globule of sap ascends; in yourself slumbers the whole of Reason… We have listened too long to the courtly muses of Europe.  The spirit of the American freeman is already suspected to be timid, imitative, tame… We will walk on our own feet; we will work with our own hands; we will speak our own minds… A nation of men will for the first time exist, because each believes himself inspired by the Divine Soul which also inspires all men.”-Ralph Waldo Emerson, “The American Scholar,” 1837In the above passage, Emerson is calling for