What is the area between the curve y=cos3x*sin-x, x axis and lines x=o and x=pi?

We'll have to calcuate the definite integral of the
function cos3x*sin(-x)

Int
cos3x*sin(-x)dx

We'll re-write cos 3x = 4(cos x)^3 - 3cos
x

We'll substitute cos x =
t

We'll differentiate both
sides:

- sin x dx = dt

We'll
re-write the integra in t:

Int (4t^3 -
3t)dtl

We'll apply the property of integral to be
additive:

Int (4t^3 - 3t)dt  = 4Int t^3dt - 3Int
tdt

4Int t^3dt - 3Int tdt = 4*t^4/4 -
3t^2/2

We'll simplify and we'll
get:

Int (4t^3 - 3t)dt = t^4 -
3t^2/2

We'll apply Leibniz-Newton
formula:

Int cos3x*sin(-x)dx = (cos pi)^4 - (cos 0)^4 -
(3/2)[(cos pi)^2 - (cos 0)^2]

Int cos3x*sin(-x)dx = (-1)^4
- 1 - (3/2)(1 - 1)

Int cos3x*sin(-x)dx =
0

The area between the given curve, x axis
and the given lines is 0 square units: Int cos3x*sin(-x)dx =
0.

How would you critically explicate lines 1-26 of Book I of John Milton's epic poem Paradise Lost?

Lines 1-26 of Book I of John Milton’s epic poem
Paradise Lost are particularly important because they announce many
of the most important themes of the poem as a whole. They also exhibit some of the
techniques, and some of the crucial words, that Milton will employ throughout the poem.
The first line, for instance, speaks of “man’s first disobedience,” referring to the
very first sin, committed by Adam and Eve in the Garden of Eden. This, of course, is a
chief theme of the entire work. Yet already Milton is playing with words, since the word
“first” implies both the priority of this sin in time as well as its crucial importance:
it was the most significant of all sins precisely because it was
the first and thus provided a pattern for every other subsequent sin. Similarly, when
Milton refers to the “fruit / Of that forbidden tree” (1-2), he puns on the word
“fruit,” referring both to the literal fruit tasted by Adam and Eve as well as to
everything that resulted from their eating of the fruit.

In
line 3, the speaker of the poem announces that the taste of the fruit “Brought death
into the world, and all our woe.” Death, of course, is another main theme of this poem,
but note that Milton uses phrasing normally associated with birth (when he speaks of
something being “Brought . . . into the world”) when he paradoxically announces the
birth of death. The first sin was also responsible for “all our woe” – a phrase that
splendidly uses assonance and heavily accented monosyllables to draw out the length of
the phrase and thus issue almost a cry of pain. The word “woe,” moreover, will be used
frequently throughout the poem, as will the word “all,” so that Milton is here
emphasizing key parts of his subsequent vocabulary.

Note
that it is not until line 6 that the verb “Sing,” on which all of the first six lines
depend, eventually appears. This kind of unusual sentence structure is often found in
Latin sentences but rarely in English, but Milton deliberately wanted to imitate a
so-called “Latinate” syntax in this poem. Milton’s “invocation” to (or calling upon) the
“Heav’nly Muse” (6) shows his desire to write a Christian epic while still using many of
the formal devices of a classical epic. Invocations to the muses were common in the
earliest Greek and Roman epics, and Milton is here showing his typical desire to imitate
the classics while also, in a sense, surpassing them.

Many
more aspects of the first 26 lines might be mentioned, such as the biblical allusion at
the beginning of line 9, the echo of an Italian epic in line 16 (a line in which Milton
paradoxically proclaims his desire to be original), and the emphatic statement of the
key theme of the entire poem in line 26 itself. Milton’s invocation is simultaneously
assertive (12-16) and humble (22-23) in a way that is characteristic of the poem as a
whole.

For an excellent brief overview of the poem, please
see C. S. Lewis, A Preface to Paradise Lost (Oxford: Oxford
University Press, 1961).

Attempt a post colonial reading of Pride And Prejudice.

This is a very interesting question. I am sure that we can
say a lot of things, but here is my attempt at your very good question. Perhaps we can
say that the dominant society is the colonial power. In this instance, we can say that
men and the social structure that they have created is the dominant power in view. They
are the ones who are spinning the ideology of what is proper. The colonized, then, are
the women. But here is the twist. The colonized see through the power dynamics and they
now begining to challenge it and even having some success. Good
luck.

What is an insight about life pertaining to justice in The Crucible?

Sometimes, we can't rely on external sources to provide
justice for us. In The Crucible, relying on the courts for true
justice did not work out too well for many people in Salem.  In act three, as John,
Francis, Giles and Mary come to the courts with firm proof and logical rationale
regarding the cases in the court at the time, the judges refused to dispense equal and
fair justice.  Innocent people were hanged, and many others unfairly jailed.  The courts
were supposed to enact justice and did not.  The message was clear:  do not rely on the
courts for justice.

Also, do not rely on others to be
just.  If everyone in the play had been just, no accusations would have been made.  In
fact, many of the accusations made were people's attempts to thwart justice's own
demands of them.  Justice would demand that Abby and the girls be punished for dancing
and casting spells; to avoid that justice, they lied and accused others.  If anyone in
Salem counted on people being kind, fair, and just, they were disappointed.  Instead,
fear, paranoia, panic, betrayal, jealousy and greed reigned
supreme.

The only true justice that occurs in the play is
the justice that people are able to bring to their own hearts.  At the end of the play,
John finally is at peace with himself.  He feels like he has finally paid for his sins,
and done enough good deeds to earn redemption.  He walks to the gallows a free man,
because he brought his own justice to his life.  He paid for his sins, he righted his
wrongs.  He was justified and at peace at the end.

The
major message is to not rely on others, or institutions for justice; it will often end
in disappointment and wrongdoing. Instead, find your own way.  I hope that helped; good
luck!

When the fire is built in Chapter 2 of Lord of the Flies, what do the little ones see in it?This a question from the chapter 2 Lord of the Flies...

I think that the answer you are looking for comes at
almost the very end of the chapter.  I think that your answer should be that the
littleuns see snakes in the fire.

The kids as a group see
lots of things in the fire.  Or at least, the fire is described in many ways.  It is
described as a squirrel climbing a tree.  It is described as a jaguar creeping
along.

But the one time that the littleuns describe what
they see, they say that they see snakes.  This happens just before they realize that the
littlun with the birthmark is missing.

Discuss four incidents from Roll of Thunder, Hear My Cry that demonstrates prejudice and injustice.This is not my homework. I want to know because...

There are many examples of racial prejudice and injustice
in Mildred Taylor's novel, Roll of Thunder, Hear My Cry. I've
included four examples:

THE
SCHOOLS.  The differences between the two schools are based on racial and
social prejudice. The all-African-American school, the Great Faith Elementary and
Secondary School, is second-class in comparison with the all-white Jefferson Davis
County School. Cassie's school gets worn-out books that are discarded from Jefferson
Davis, and the white children are bused to school, while the black kids have to
walk.

THE BERRYS.  John
Henry Berry and his two nephews are deliberately set afire by a group of white "night
riders." Mr. Berry dies from his
injuries.

MR.
MORRISON.  The Logan family friend, Mr. Morrison, relates
how he was fired from his job. He got into a fight with two white men and, although they
started the fight, only Morrison was fired because he was
black. 

THE BUS DRIVER.  A
white bus driver for the Jefferson Davis school deliberately "bears down" on several
black children, who are forced to jump into a muddy ditch. The white kids on the bus
taunt the black kids with shouts of "Nigger!"

These are
only four examples, and they all take place in the first three chapters of the novel.
Sadly, there are many more to be discovered.

Solve the equation if x is in interval (0;2pi) cos3x=cosx

First of all, we'll try to calculate cos 3x = cos
(2x+x)

cos (2x+x) = cos 2x*cos x - sin x*sin
2x

sin (2x) = 2sin x*cos x

cos
2x = 2 (cos x)^2 - 1

cos 3x = [2 (cos x)^2 - 1]*cos x - 2[1
- (cos x)^2]*cos x

cos 3x = 4(cos x)^3 - 3cos
x

So the equation will
become:

4(cos x)^3 - 3cos x= cos
x

We'll move all terms to one
side:

4(cos x)^3 - 3cos x- cos x =
0

4(cos x)^3 - 4cos x =
0

We'll factorize by
4cosx:

4cos x*[(cos x)^2 - 1] =
0

4cos x = 0

cos x =
0

The values of the angle x, located in the range (0 ;
2pi), for the function cosine is 0, are: x = pi/2 and x =
-pi/2.

(cos x)^2 - 1 = 0

Since
it is a difference of squares, we'll re-write it as a
product:

(cos x - 1)(cos x + 1) 
=0

cos x - 1 = 0

cos x =
1

The values of the angle x, located in the range (0 ;
2pi), for the function cosine is 1, are: x = 0 and x
=2pi.

Neither of these values are located in the given
range, since the interval is opened both sides, meaning that the values 0 aand 2pi are
not included.

cos x + 1 =
0

cos x = -1

The value of the
angle x, located in the range (0 ; 2pi), for the function cosine is -1, is: x =
pi.

The solutions of the equation, located in
the interval (0 ; 2pi),are: {pi/2 ; pi ; 3pi/2}.