Evaluate the definite integral of f=1/(x^2+2x+5) from 0 to 1 .

To evaluate the definite integral, we'll re-write the
denominator.

x^2+2x+5 =
x^2+2x+4+1

We'll group the terms: x^2+2x+1 =
(x+1)^2

The denominator will
become:

(x+1)^2 + 4

We'll
write the integral:

Int f(x)dx = Int
dx/(x^2+2x+5)

Int dx/(x^2+2x+5) = Int dx/[(x+1)^2 +
4]

We'll substitute x+1 by
t.

x+1 = t

(x+1)' =
1*dx

t' = dt

So, dx =
dt

We'll re-write the integral in
t:

Int dx/[(x+1)^2 + 4] = Int
dt/(t^2+4)

We'll factorize by 4, at
denominator:

Int dt/4(t^2/4 + 1) = (1/4)*Int dt/[(t/2)^2 +
1]

(1/4)*Int dt/[(t/2)^2 + 1] = 2/4*arctg (t/2) =
(1/2)*arctg (t/2)

But t =
x+1

For x = 0 => t =
1

For x = 1 => t =
2

Now, we'll apply Leibniz-Newton
formula:

Intdx/(x^2+2x+5), from 0 to 1 = F(2) -
F(1)

F(2) = (1/2)*arctg (2/2) =
(1/2)*(pi/4)

F(1) = (1/2)*arctg
(1/2)

F(2) - F(1) = (1/2)*[pi/4 - arctg
(1/2)]

Intdx/(x^2+2x+5), from 0 to 1 =
(1/2)*[pi/4 - arctg (1/2)]

What are the themes of Dairy Queen by Catherine Gilbert Murdock?Is there another theme to Dairy Queen besides (needing to speak up for yourself)?...

You could expand the communication theme into an idea
about how communication affects relationships.  Look at DJ's father - and how he
communicates differently with his children and then with his
wife.

Another theme you could tap into is the idea of
traditional gender roles and the way this book presents them so untraditionally.
 Consider that main character, DJ, first must take over her family farm when her father
gets hurt.  This is usually reserved for a son, but she is the oldest... then, she's put
in charge of training a quarterback for a football team.  Not expected.  This of course
leads her to trying out for the football team herself - a decision she grapples with for
a long time - especially when she considers how it will make her father feel.  The
communication theme is the most central - but if you were looking for something a little
less obvious - I think you could do a great job discussing the breaking-out of
traditional gender roles.

Finally, I think you could talk
about the theme of growing up, becoming comfortable with who you are and discovering how
roles change when relationships change.  DJ is clearly a bit of a tomboy.  She isn't
uncomfortable saying the things other girls might never say (like blurting out that
Brian needs a trainer, not a job.)  She is completely comfortable with her role as his
"trainer" but things change dramatically when she starts to fall for him romantically.
 This theme is a little more generic - I think it could be applied to almost any Young
Adult fiction novel - so it might not be my first choice for an essay, for example, but
if you just needed a list, it would be one to add.

Describe Emily Bronte's style (diction, syntax and tone) in Wuthering Heights.

One of Bronte's many writing talents was her particular
use of language. The tone is a description of the speaker's attitude towards his
subject, and is best described by an adjective. The tone in Wuthering
Heights shifts with the narrator. Our first narrator is Lockwood, and
understanding his characterization, he is Heathcliff's new tenant, someone who is
excited to be living in new property (Thrushcross Grange). His attitude at the very
beginning of the novel can be described as enthusiastic, indicating to the reader the
ironic tone, which we can analyze through the use of diction and syntax. In the very
first chapter, Lockwood describes the state of Wuthering Heights
as:

A perfect
misanthrope's Heaven - and Mr. Heathcliff and I are such a suitable pair to divide the
desolation between us.

Bronte
gives Lockwood the insight to pick up on the isolation of Wuthering Heights, and her
decision to use "misanthrope" is ironic because though Lockwood can physically see the
setting is spacious and far from the city, he is not yet aware of how misanthropic
Heathcliff truly is; Lockwood is much more intuitive than he realizes at the moment. To
add to the irony, Bronte's syntax - the use of the dash - demonstrates how Lockwood,
again unaware of his true surroundings, compares his jolly self to Heathcliff.
Heathcliff is monsterous at this point of the novel (before the flashbacks), and
Lockwood is young and jocund, ready to begin his life.

The
tone shifts when Lockwood realizes Heathcliff's nature, and he encounters Cathy's ghost,
moving from ironic to nervous and desolate, giving the reader an insight on what it is
like to be one of Heathcliff's "prisoners."

Nelly becomes
the narrator, and she is a bit more objective, having seen Heathcliff and Cathy grow up
together. The tone shifts between desperate, compassionate, and a strong sense of
foreboding, as Nelly is aware of the true love between Cathy and Heathcliff, along with
understanding their final outcomes.

With a focus on
diction, Cathy describes her relationships to nature, using words such as "foliage" for
Linton and "rocks" for Heathcliff, indicating that her feelings for Linton are temporary
and ethereal, while her feelings for Heathcliff are stubborn, unmoving, and
surefire.

What is the theme of "Why I Live at the P.O."?

A theme of “Why I Live at the P.O.” is that
sometimes a lie is better than the
truth.

This story is about a family
squabble.  Sometimes families have to tell each other lies, and accept believing one
another’s lies, in order to keep the peace and save face.  Stella-Rondo had to leave her
husband Mr. Whitaker.  She is trying to make the best of the situation by telling
everyone that her daughter Shirley-T is adopted.  The narrator refuses to believe this
lie, but all of the other family members seem to accept
it.

readability="13">

Stella-Rondo just calmly takes off
this hat, I wish you could see it. She says, "Why, Mama,
Shirley-T.'s adopted, I can prove it."
 "How?" says Mama, but all I says was,
"H'm!"

Mama seems willing to
accept this explanation, and the other family members accept Shirley-T.  The narrator
does not, and Stella-Rondo is annoyed at her and uses it to turn things she says against
her to antagonize other members of the family, such as when she says the narrator wanted
to know why Papa-daddy did not shave his beard.  Papa-daddy is very proud of his beard,
and this infuriates him.  The narrator denies it, but he continues to believe
Stella-Rondo.

Family members’ continued acceptance of
Stella-Rondo’s word over the narrator’s is an example of how they have accepted that
sometimes it is better to tell a little lie than to tell the truth.  If Stella-Rondo
admitted that she had a child out of wedlock, it would be intolerable for other family
members.  It is much easier for everyone to accept both of them into family and ignore
the narrator’s objections.

In Of Mice and Men, why does Curley pick a fight with Lennie, the strongest of all the men, instead of George?

punk," he
said. "You tried to throw a scare into Slim, an' you couldn't make it stick. slim
throwed a scare inta you. You're yella as a frog belly. I don't care if you're the best
welter in the country. You come for me, and I'll kick your God damn head
off."

For somebody who is as
proud and arrogant as Curley, this is unacceptable and so he seeks to find an easy
target that he can take his anger out on and also convince himself that he is no as
"yella as a frog belly." Lennie is still lost in his daydream of the farm, and smiling
abstractedly, thus Curley thinks he is laughing at him and picks him. It is because of
the context of being made fun of that Curley feels he has to prove
himself:

Then
Curley's rage exploded. "Come on, ya big bastard. Get up on your feet. No big
son-of-a-bitch is gonna laugh at me. I'll show ya who's
yella."

This of course ends
in even further humiliation for him as Lennie

Of course,
the context of this passage is key to understanding why it is that Curley picks on
Lennie. He is being made fun off by the other men in the ranch because they recognise
how weak he actually is as a character. Note what Carlson says to Curley just before he
turns to
Lennie:

For
somebody who is as proud and arrogant as Curley, this is unacceptable and so he seeks to
find an easy target that he can take his anger out on and also convince himself that he
is no as "yella as a frog belly." Lennie is still lost in his daydream of the farm, and
smiling abstractedly, thus Curley thinks he is laughing at him and picks him. It is
because of the context of being made fun of that Curley feels he has to prove
himself:

Then
Curley's rage exploded. "Come on, ya big bastard. Get up on your feet. No big
son-of-a-bitch is gonna laugh at me. I'll show ya who's
yella."

This of course ends
in even further humiliation for him as Lennie

Of course,
the context of this passage is key to understanding why it is that Curley picks on
Lennie. He is being made fun off by the other men in the ranch because they recognise
how weak he actually is as a character. Note what Carlson says to Curley just before he
turns to Lennie:

readability="10">

Carlson laughed. "You God damn punk," he said.
"You tried to throw a scare into Slim, an' you couldn't make it stick. slim throwed a
scare inta you. You're yella as a frog belly. I don't care if you're the best welter
in the country. You come for me, and I'll kick your God damn head
off."

For somebody who is as
proud and arrogant as Curley, this is unacceptable and so he seeks to find an easy
target that he can take his anger out on and also convince himself that he is no as
"yella as a frog belly." Lennie is still lost in his daydream of the farm, and smiling
abstractedly, thus Curley thinks he is laughing at him and picks him. It is because of
the context of being made fun of that Curley feels he has to prove
himself:

Then
Curley's rage exploded. "Come on, ya big bastard. Get up on your feet. No big
son-of-a-bitch is gonna laugh at me. I'll show ya who's
yella."

This of course ends
in even further humiliation for him as Lennie

Discuss specifically the possible symbolism of the elements in "The Lottery."Discuss the description of the black box; the description of the...

A haunting short story, Shirley Jackson's "The Lottery"
juxtaposes ordinary circumstances and activities with ones that are macabre.  Even in
her use of symbols, the ordinary become darkly significant.  For instance, Mrs.
Hutchinson's apron that in her haste she has forgotten to remove represents ordinary
daily life that is measured against the black spot that is on her slip of paper, marking
her abruptly for death.

The black
box, is splintered badly along one side, and grows shabbier every year,
yet this coffin-like box is pulled out every year because it is part of a tradition. 
Representing death, it is placed upon the three-legged stool by Mr. Summers and the
villagers "kept their distance, leaving a space between themselves and the stool" in
their fear of its ominous portent.

The
ceremony of drawing lots is symbolic of the ancient custom of finding a
scapegoat for the evils of the village.  By sending a scapegoat out into the desert to
die, the rest of the village would be saved from bad luck.  But, now, much of "the
ritual had been forgotten or discarded," so Mr. Summers has slips of paper substituted
for the chips of wood that were formerly used. Whereas there was formerly a ritual
salute and some procession, much has been "allowed to lapse."  But, the drawing of the
lottery is performed yearly simply because it is customary: When Mrs. Adams says, "Some
places have already quit lotteries," Old Man Warner says
"stoutly,"

readability="5">

"Nothing but trouble in
that....Pack of young
fools." 

Clearly, Mr. Warner
believes in the lottery simply because it is
tradition.

The pile of
stones, those "symbols of preposterous time" as Golding writes
in Lord of the Flies, lies waiting for the victim.  The stones
represent the ancient and intrinsic predilection of people for violence and sadistic
pleasure.  Striking with stone after stone becomes an unthinking brutal act, a primitive
ritual, that is part of their natures: 

readability="7">

Although the villagers had forgotten the ritual
and lost the original black box, they still remembered to use
stones.

Women in prison, their treatment, prison conditions, and the programs offered to women in prison?Discuss the prison changes from the 1800's to...

People in general are treated better in prison today than
they were in the 1800's. In the late 1700's and early 1800's, prisoners were often
treated very poorly. They were seen as "wild animals" and many times
tortured.

Females, in particular, had different roles back
then as well. If a woman was a prisoner she was breaking not only written law, but the
unwritten laws as well. Women were second class citizens compared to men. They were
usually housed with the general population (children as well) and often ended up
prostituting themselves out, just to survive. Living conditions were very bad. Prisons
today are much different. Prisons offer many different rehabilitation programs, quality
food, and medical/dental coverage.

I am attaching a link
below to a very interesting article that I came across. It discusses prisons of today,
as well those from the 1700's and 1800's.