`int x tan^2(x) dx` Evaluate the integral

`intxtan^2(x)dx`

Let's evaluate the above integral by using the method of integration by parts,

If f(x) and g(x) are differentiable functions , then

`intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx`

If we write f(x)=u and g'(x)=v, then

`intuvdx=uintvdx-int(u'intvdx)dx`

Let's denote u=x and `v=tan^2(x)`

`intxtan^2(x)dx=x*inttan^2(x)dx-int(1inttan^2(x)dx)dx`

Now let's use the identity:`tan^2(x)=sec^2(x)-1`

`=x*int(sec^2(x)-1)dx-int(int(sec^2(x)-1)dx)dx`

`=x*(intsec^2(x)dx-int1dx)-int(int(sec^2(x)-1)dx)dx`

`=x*(tan(x)-x)-int(tan(x)-x)dx`

`=xtan(x)-x^2-inttan(x)+intxdx`

`=xtan(x)-x^2-(-ln|cos(x)|)+x^2/2`

`=xtan(x)-x^2+x^2/2+ln|cos(x)|`

`=xtan(x)+ln|cos(x)|-x^2/2`

Add a constant C to the solution,

`=xtan(x)+ln|cos(x)|-x^2/2+C`

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When did the Minoan (Thera) volcanic eruption occur?

There is a considerable amount of debate surrounding the time frame of the Minoan, also known as the Thera, eruption. Evidence for the eruption itself is found throughout the Eastern Mediterranean region. Most scholars date the Minoan eruption between 1627BCE and 1590 BCE.

Radiocarbon dates, thought to be the most accurate dating techniques applied to evidence of the Minoan eruption, suggest that the volcano's activity reached its peak between 1627-1600BCE (see Friedrick et al., 2006, Science Magazine). Using an olive tree branch, this team was able to narrow the 95% confidence interval to a smaller time frame than previously suggested.

In fact, the only other leading school of thought is led by archaeologists who date the Minoan eruption to approximately 1500BCE based on artifacts collected at the study site. Although chemical dating is typically thought to be the most accurate method of creating a timeline for something like a volcanic eruption, qualitative evidence suggests that the chemical process may be yielding incorrect results.

Is Harrison in "Harrison Bergeron" a hero, criminal, rebel, or revolutionary?

If you were to ask this question to the characters of “Harrison Bergeron,” you would receive very different answers. Harrison would see himself as a hero and revolutionary. Upon taking over the television studio, he proclaims himself emperor and makes it clear that his intention is to overthrow both the government and its draconian laws regarding equality. To Harrison, his actions are justified by the multiple handicaps the government has put on him to dull his intelligence, strength, and natural handsomeness.  

To someone like Handicapper General Diana Moon Glampers, on the other hand, Harrison is a criminal and a rebel. To her, Harrison stands against the established order that she represents. Killing Harrison is not only a punishment for his treason, but a public suppression of dissent that sends a clear signal to any would-be Harrisons watching the events unfold on television.

What are positives and negatives for absolute monarchy?

It is easy for us to think of the negative aspects of an absolute monarchy.  We live in a democratic country and so we have been told ever since we were young why monarchy is bad and democracy is good.  One major reason for this is that, in an absolute monarchy, no one has any guaranteed rights.  The monarch has the right to do whatever he or she wants at any time.  The monarch could take your land or other property.  They could throw you in jail because they did not like what you had said.  There was no guarantee of any sort of rights because the monarch was all-powerful.  The second major problem is that there is nothing to protect the people and the country from the whims of a bad absolute monarch.  If the absolute monarch is a bad person, or simply has harmful ideas, there is no defense.  There is no one to stop the monarch from getting their way.  The monarch can, without anyone to check them, enact policies that are evil or policies that are simply destructive and harmful.  These are the main negative aspects of having an absolute monarchy and they are very powerful arguments against such a system of government.

However, we can say that there was at least one good thing about having absolute monarchy.  The greatest positive point about this system is that ensured that things in a country could get done quickly and efficiently.  Here in the United States, we have a political system that prevents the government from doing anything quickly.  Our system has all sorts of checks and balances that make it hard to get things done.  For example, we all know that something needs to be done to our system of entitlements, but our leaders cannot agree on what to do so nothing gets done.  The same is true of our tax code.  In an absolute monarchy, this does not happen.  If the monarch has an idea, that idea can be implemented very quickly because there is no one to say “no” to the monarch.  Right now, that might look good to some Americans who feel frustrated by the lack of action by our democratic government.

So, the great thing about an absolute monarchy is that it can get things done quickly.  However, the flip side of this is that the monarch can do terrible things (or just misguided things) just as easily as they can do good things.  This means that the absolute monarchy is efficient, but it also means that there is nothing to mitigate the harm that a bad absolute monarch can do to the country.

Why does producing a single bacterium through genetic recombination enable researchers to produce large numbers of bacteria with the recombined...

Because bacteria reproduce! They are alive!

It's difficult to overstate how momentous an achievement it is that in recent years we have been able to cross that threshold into creating synthetic lifeforms. Very simple lifeforms, mind you; all bacteria. But life. We have crossed a threshold in the evolution of our civilization that is nothing less than Promethean---it belongs on a list with fire, the wheel, the steam engine, the atom bomb. Synthetic biology will open previously unimaginable applications, with tires that self-heal so they never go flat and bandages that grow directly into your skin to become incorporated as permanent tissue being some of the most mundane. More radical applications include terraforming Mars and living computers.

Bacteria not only reproduce, they reproduce extraordinarily fast. The famous E. coli can divide itself about once every 20 minutes, which creates exponential growth that is only constrained by the available nutrient substrate (usually agar in a petri dish).

So, if you start with one synthetic bacterium, in 20 minutes you have 2. In 40 minutes you have 4. In an hour you have 8. Not so impressive, right?

Ah, but wait. In 2 hours you have 64. In 3 hours, 512. In 4 hours, 4,096. By the end of an 8-hour workday you have over 16 million, and I guarantee you that when you come back in the morning your petri dish will be filled, no matter how big it is, because if the exponential growth had been allowed to continue then within 24 hours the bacteria would have engulfed the Earth.

Thus, creating that one bacterium might be more difficult than even making thousands of the plasmid we want by more direct means---but once it reproduces, the bacterium won't give us thousands---it will give us millions, billions, or even trillions.

What food item became currency for the trade system among the confederate prisoners?

Most people don't consider rats a food item, but if they were among the over 400,000 soldiers held prisoner during the U.S. Civil War, they might change their mind. Desperation led to desperate schemes in POW camps in both the North and the South. One soldier at  Camp Lawton, near Millen, Georgia, wrote that prisoners were “obsesses with food, sometimes consuming rats or boiling grass to ward off scurvy” (quoted in CNN.com/us/civil war/150th anniversary-prisons).

Of all the prison camps, Andersonville Prison in the Confederate State of Georgia is the most well known, and it was considered the worst of all camps. About 45,000 soldiers went through Andersonville. The peek population, in a prison built to house only 10,000, was over 33,000. And when the prisoner swap between the Northern and Southern Armies stopped because the South refused to exchange “negro troops the same as white soldiers,” the overcrowded conditions continued (civilwar.org). Food was scarce for everyone in the prisons, prisoners and guards alike. However, the guards were fed more of the scarce rations than the prisoners, so prisoners ate whatever they could find — including rats. Lack of adequate food, medical care, and sanitation took the lives of many at the Andersonville Prison Camp.

Overcrowding was an issue in almost all prison camps during the war, in both the North and the South. Thus, insufficient food was also a problem for overcrowded Northern POW camps. The Elmira Camp in the Union State of New York, with barracks space for only 5,000, had 12,000 prisoners residing there between July 6,1864, and July 11,1865. Hence, the prisoners in Northern camps also ate whatever they could find. Rats were a big problem at the camps, so the Elmira Camp officials used a small dog to catch rats that they then sold to prisoners for 5 cents. Most of the Confederate soldiers could not afford the 5 cents, though, leading two Elmira prisoners to capture the dog and cook it. They were, of course, sent to the guardhouse for 30 days for punishment.

Countless soldiers on both sides died from malnutrition and disease, especially since there was little medical care available. At Elmira about one-fourth (3,000) of the prisoners died. At Andersonville, over 12,000 died (almost as many as the whole prison population at Elmira). Approximately 56,000 deaths, nearly 10% of the total Civil War death toll, were due to the horrible conditions in prison camps.

How can you explain the rise of Napoleon?

Several factors led to Napoleon’s rise to power. First, Napoleon’s success directly correlates to the French Revolution because such a political climate enabled Napoleon, despite his modest upbringing, to become an Emperor. While in years prior only the elite could participate in the government, the French Revolution challenged long-held ideals which favored the aristocracy's sole involvement in politics and matters of the state. Accordingly, someone like Napoleon was actually allowed (and encouraged) to enter the political arena. At the same time, Napoleon was a gifted military strategist, and after his initial rise to power, he demonstrated his talents in various military campaigns in Italy and Egypt. In 1799, Napoleon and his supporters overthrew the Directory Government of France, thus officially marking Napoleon’s reign. Napoleon was also married to Josephine, whose well-connected Father was a member of the Directory Government. This relationship allowed Napoleon access to the inner workings of the state, while also contributing to Napoleon’s popularity with the masses. In short, the unstable political landscape in France, Napoleon’s ambitious nature, and political/personal affiliations all paved the way for his popularity and subsequent reign.