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The Doll's HouseIn Mansfield's "The Doll's House," the Burnell children are not allowed to associate with the Kelvey girls. The Burnell girls are members of the upperclass and a family friend (Mrs. Hay) has sent...

Wuthering HeightsThe roots of ambition in Wuthering Heights are present in both Heathcliff and Catherine. Heathcliff, who is taken off the street by Mr. Earnshaw, is mistreated by everyone in the family except his...

The RavenHow do poetic devices and figurative language efftect the reader's understanding of Gothic themes...To state that Edgar A. Poe was very fond of the Gothic mode may sound like a commonplace, since there are myriad of scholarly studies in the subject. What is not so often acknowledged is the fact...

HistoryThe Progressives’ views on regulating business were that government should regulate business so that businesses could not abuse the people. They felt that businesses used their economic power to...

HistoryThe reason the Third Estate paid all the taxes under the Bourbon monarchy in France is that the kingdom had an inefficient, outdated tax system. Nobles and clergy received many privileges, one of...

MacbethFirst of all, he demonstrates his arrogance by demanding that the witches answer his questions. One might think Macbeth would express some humility or even cautiousness before these supernatural...

The Canterbury TalesIrony is, generally, the difference between what you expect to happen and what really happens. In the case of Chaucer's "The Pardoner's Tale," from The Canterbury Tales, dramatic irony is used....

ScienceSpecific heat and latent heat are intensive material properties. Intensive properties are properties of a material which don't vary depending on the amount of mass present. For example, if a block...

The Masque of the Red DeathWhen the striking of the great ebony clock announces midnight, the revelers halt and there is "an uneasy cessation of all things as before," signifying the guests' recognition of the force of time...

BusinessIn my view, it does not make sense for employers to be allowed to file grievances, at least if we are talking about grievances filed against workers or the union. This is because the employers...

Everyday UseDee has gone out into the world and become successful. We don't exactly know what all she has succeeded at, but we do know she has had a very good education that her mother has paid for at great...

Of Mice and MenBoth Lennie and George are wearing clothing appropriate for traveling ranch workers: denim, black hats, and blankets to sleep on  wherever they happen to rest. The physical descriptions of each...

LiteratureAll segregation, whether it is residential, social, educational, financial or political, always causes those who are set apart from having equal opportunities and advantages in society. For Walter...

The Healers[First, please note that I have corrected the misspelled character name from “Araba Jessiwa” to Araba Jesiwa.] Literary techniques in the subject of Literature are many and varied because they...

LiteratureKill Shakespeare is a 12issue comic book series created by Conor McCreery and Anthony Del Col with the purpose of helping a large audience better appreciate Shakespeare and to learn more about...

To Kill a MockingbirdSheriff Tate’s expression of “let the dead bury the dead” is another way of saying “put this matter to rest.” In hopes of returning Maycomb back to its normal, everyday routine, Sheriff...

MathWe have to be careful here because of absolute value sign. We need to know where the function under absolute value changes sign (in the interval of integration), which is at `x=pi` in this case....

MathHello! Find the indefinite integral: `int((sqrt(y)y)/y^2)dy=int(y^(3/2)1/y)dy=(2)*y^((1)/(2))ln(y).` Then substitute y from 1 to 4: `(2*4^(1/2)ln(4))(2)=1ln(4)+2=1ln(4) approx 0.386.`

MathHello! First find the indefinite integral, `int(x/(2)2/x)dx=int(x/2)dxint(2/x)dx=(x^2)/42ln(x).` Then substitute x from 1 to 2: `(2^2/42ln(2))(1^2/42ln(1))=12ln(2)1/4=3/42ln(2) approx...

MathYou need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_0^1(5x  5^x)dx = int_0^1(5x)dx  int_0^1 5^x dx`...

MathYou need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_0^1(x^10 + 10^x)dx = int_0^1(x^10)dx + int_0^1 10^x...

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that: `int_a^b f(u) du = F(b)  F(a)` `int_(pi/4)^(pi/3) csc^2 theta d theta = int_(pi/4)^(pi/3) 1/(sin^2...

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that:` int_a^b f(x)dx = F(b)  F(a)` `int_0^(pi/4)(1+cos^2 theta)/(cos^2 theta) d theta =...

MathBefore evaluating this integral, simplify the expression in the integral using trigonometric identities. The following Pythagorean identity will be useful: `tan^2(theta) + 1 = sec^2(theta)` Start...

MathWe will make substitution `x=t^6.` Therefore, the differential is `dx=6t^5dt` and the new bounds of integration are `t_1=root(6)(1)=1` and `t_2=root(6)(64)=2.` `int_1^64(1+root(3)(x))/sqrt x...

MathHello! Consider the denominator first: `sinh(x)+cosh(x)=(e^xe^(x))/(2) +(e^x+e^(x))/(2)=e^x.` Therefore the integrand is equal to `2` and the integral is 2*(10(10))=40.

MathHello! This integral is a table one, `int(dr)/(sqrt(1r^2))=arcsin(r)+C.` ` ` Therefore the definite integral is equal to `arcsin(sqrt(3)/2)arcsin(0)=pi/30=pi/3 approx 1.047.` =arcsin(r)+C.

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` You need to expand the cube such that: `(x1)^3 = x^3  1  3x(x1)...

MathHello! `(t^21)/(t^41)=1/(t^2+1).` Therefore indefinite integral is `arctan(t)(+C).` Substitute t from 0 to `1/sqrt(3)` and obtain `arctan(1/sqrt(3))arctan(0)=pi/60=pi/6 approx 0.524.`

MathWe have to be careful because of the absolute value. We need to know where the function under absolute values is positive and when it is negative in the given interval. It is also a good idea to...

MathHello! Consider two intervals: (1, 0) and (0, 2) to simplify x: `int_(1)^2(x2x)dx=int_(1)^0(x2x)dx+int_0^2(x2x)dx=` `=int_(1)^0(x+2x)dx+int_0^2(x2x)dx=`...

MathYou need to find the indefinite integral, hence, you need to remember that `sec t = 1/(cos t)` , such that: `int (sec t)(sec t + tan t) dt = int (1/(cos t))(1 + sin t)/(cos t) dt` `int (sec t)(sec...

MathYou need to find the indefinite integral, hence, you need to remember that `1 + tan^2 x = 1/(cos^2 x) = (tan x)'.` `int (1 + tan^2 x )dx = int (tan x)' dx = tan x + c` Hence, evaluating the...

MathYou need to find the indefinite integral, hence, you need to remember that sin `2x = 2sin x*cos x` , such that: `int (sin 2x)(sin x) dx = int (2sin x*cos x)/(sin x) dx ` `int (sin 2x)(sin x) dx =...

MathYou need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_(2)^3(x^3  3)dx = int_(2)^3(x^3)dx  int_(2)^3 3...

MathYou need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_1^2(4x^3  3x^2 + 2x)dx = int_1^2(4x^3)dx  int_1^2...

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_(2)^0 ((1/2)t^4 + (1/4)t^3  t)dt = int_(2)^0 ((1/2)t^4 dt +...

MathWe will use linearity of integral: `int(a cdot f(x)+b cdot g(x))dx=a int f(x)dx+b int g(x)dx.` `int_0^3(1+6w^210w^4)dw=int_0^3dw+6int_0^3w^2dw10int_0^3w^4dw=`...

MathWe have to evaluate the integral: `\int_{0}^{2}(2x3)(4x^2+1)dx=\int_{0}^{2}(8x^312x^2+2x3)dx` `=[8(x^4/4)12(x^3/3)+2(x^2/2)3x]_{0}^{2}`...

MathYou need to use the following substitution to evaluate the definite integral, such that: `1  t = u => dt = du` `int_(1)^1 t*(1t)^2dt = int_(u_1)^(u_2) (1  u)*u^2 (du)` `int_(u_1)^(u_2) (u...

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_0^pi (5e^x+ 3sin x)dx = int_0^pi 5e^x dx + int_0^pi 3sin x...

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_1^2 (1/x^2  4/x^3)dx = int_1^2 1/x^2 dx  int_1^2 4/x^3 dx`...

Math`int_1^4(4+6u)/sqrt(u)du` `=int_1^4(4/sqrt(u)+(6u)/sqrt(u))du` `=int_1^4(4u^(1/2)+6u^(1/2))du` `=[4(u^(1/2+1)/(1/2+1))+6(u^(1/2+1)/(1/2+1))]_1^4` `=[4(u^(1/2)/(1/2))+6(u^(3/2)/(3/2))]_1^4`...

MathYou need to evaluate the definite integral using the fundamental theorem of calculus, such that: `int_a^b f(x)dx = F(b)  F(a)` `int_0^4(3sqrt t  2e^t)dt = int_0^4 3sqrt tdt  int_0^4 2e^t...

MathYou need to evaluate the definite integral, such that: `int_0^1 x(root(3) x + root(4) x)dx = int_0^1 (x^(1+1/3) + x^(1+1/4))dx` `int_0^1 x(root(3) x + root(4) x)dx = ((x^(2+1/3))/(2+1/3) +...

MathYou need to evaluate the indefinite integral, such that: `int f(x)dx = F(x) + c` `int (x^2  x^(2))dx = int (x^2)dx  int x^(2) dx ` Evaluating each definite integral, using the formula `int x^n...

Math`int sqrt(x^3)root(3)(x^2) dx` Before evaluating, convert the radicals to expressions with rational exponents. `= int x^(3/2)*x^(2/3) dx` Then, simplify the integrand. Apply the laws of exponent...

Math`int (x^41/2x^3+1/4x2)dx` To evaluate this integral, apply the formulas `int x^n dx=x^(n+1)/(n+1) +C` and `int adx = ax + C` . `int (x^41/2x^3+1/4x2)dx` `=x^5/5  1/2*x^4/4 + 1/4*x^2/22x...

Math`int (y^3+1.8y^22.4y)dy` To evaluate this integral, apply the formula `int x^n dx = x^(n+1)/(n+1) + C` . `= y^4/4 + 1.8y^3/3  2.4y^2/2 + C` `=0.25y^4 + 0.6y^3  1.2y^2 + C` Therefore, `...

MathYou need to evaluate the indefinite integral, hence, you need to open the brackets, such that: `(u+4)(2u+1) = 2u^2 + 9u + 4` `int (u+4)(2u+1) du = int (2u^2 + 9u + 4) du ` `int (u+4)(2u+1) du =...