eNotes Homework Help is a way for educators to help students understand their school work. Our experts are here to answer your toughest academic questions! Once it’s posted to our site, your question could help thousands of other students.
Popular Titles
Showing in

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reason the Third Estate paid all the taxes under the Bourbon monarchy in France is that the kingdom had an inefficient, outdated tax system.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...

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...

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...

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 =...

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...

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.`

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...

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=`...

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`...

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 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 =...

MathYou need to evaluate the indefinite integral, such that: `int f(theta)d theta = F(theta) + c` `int (theta  csc theta* cot theta)d theta = int theta d theta  int (csc theta* cot theta)d theta`...

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_0^3 (2sin x  e^x) dx =int_0^3 2sin x dx  int_0^3 e^x dx`...

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/(sqrt3))^(sqrt 3) 8/(1+x^2) dx = 8 int_(1/(sqrt3))^(sqrt 3)...

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_1^2 (4+u^2)/(u^3) du = int_1^2 4/(u^3) du + int_1^2 (u^2)/(u^3)...

HistoryThere are many different ways to answer this question. Let us look at a few. One way to answer this is to say that Thanksgiving is celebrated as a way of emulating the Pilgrims who were some of...

PoliticsThe problem with defining the term "extremist political organization" is that it is by nature one applied only in the second or third person. In other words, the word "extremism" is one we do not...

Social SciencesCompatibilism attempts to resolve the problem of free will and determinism by proposing that the two positions are compatible. Specifically, it asserts that: Determinism is true, that is, all human...

HistoryLincoln's Thanksgiving Proclamation, which declared the final day of November a national day of "thanksgiving and praise to Almighty God," was one of many similar declarations by American...

HealthTo evaluate an article from the perspective of what you and I find confusing or surprising about the content, we usually have to ask ourselves certain questions: 1)Does the author state his/her...

Of Mice and MenCrooks is the only farmhand who is African American. Living as a black man in the Depression Era, and among a bunch of rogue men of their generation, rendered Crooks as an outsider to the group....

HistoryThis phrase is found in the opening passage of the Declaration, where Jefferson is explaining why a declaration is needed in the first place. In this context "station" means something like "status"...

ScienceThe term "mRNA" stands for "messenger RNA". This is usually enough of a hint to remember their function; to carry messages in the body, specifically messages for creating proteins. The mRNA is like...

HistoryThe word "imperialism" describes a process where a nation attempts to expand its influence beyond its own borders by gaining control of territories or peoples. This can come in a number of...

Winter DreamsDexter's general feeling about winter is that it engulfs and shadows the beauty of summertime. In the story, we read that Dexter usually breaks out his skis when 'the long, Minnesota winter shut(s)...

On My First SonBefore I answer that question, let's review the definition of "tone". Tone is a literary device that indicates the emotion the author intends to communicate in his/her work, conveyed through word...

A Doll's HouseMain Theme The most salient common theme shared among the female characters found in the short story "The Yellow Wallpaper" by Charlotte Perkins Gilman, the play A Doll's House by Henrik Ibsen, and...

HistoryHow was America's society and political structure different than England's in the late eighteenth...The social structure of the American colonies was far less stratified than that of Great Britain. While there were extremes of wealth, as in the Hudson River Valley, the South Carolina Low Country,...

ScienceGood question. On the surface, they both appear to be very similar, because both ionization energy and electron affinity both deal with an atom's ability to do something with electrons. The...

Carl SandburgThat line was written by the American poet Carl Sandburg. The line is the opening line from his poem "Offering and Rebuff." The poem is quite short, but the opening stanza is a beautiful...