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

ReferenceThis is entirely possible to do. The strategy I would use is outlining. When I was in law school, there was only one exam for each course, the final exam, and I had to study 16 weeks of material...

The GiverThere are a few reasons for the Giver to feel this way. First, there is the sheer quantity and age of memories he must hold. Second, it is a burden to hold memories and never be able to share...

To Kill a MockingbirdScout explains Walter's situation to Miss Caroline because Miss Caroline is not from Maycomb and does not understand Walter's background. Miss Caroline offers Walter a quarter to buy lunch for the...

To Build a FireThe natural setting of the brutal arctic conditions of the Klondike, conditions which are indifferent to the presence of a man, express Naturalism, a literary movement among novelists who viewed...

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...

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the Third Estate paid all the taxes under the Bourbon monarchy in France is that the kingdom had an inefficient, outdated tax system.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

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...

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...

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.`

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...

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 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 =...

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)...

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_(pi/6)^pi sin theta d theta = cos theta_(pi/6)^pi`...

MathYou need to evaluate the definite integral such that: `int_1^9 sqrt x dx = (x^(3/2))/(3/2)_1^9` `int_1^9 sqrt x dx = (2/3)(9sqrt9  1sqrt1)` `int_1^9 sqrt x dx = (2/3)(271)` `int_1^9 sqrt x dx...

MathYou need to evaluate the integral, such that: `int_(1)^2(x^3  2x)dx = int_(1)^2 x^3 dx  int_(1)^2 2x dx` `int_(1)^2(x^3  2x)dx = (x^4/4  x^2)_(1)^2` `int_(1)^2(x^3  2x)dx = (2^4/4  2*2...

Math`int_(1)^1 x^100 dx` To evaluate this, apply the formula `int x^n dx = x^(n+1)/(n+1)` . `= x^101/101 _(1)^1` Then, plugin the limits of the integral as follows `F(x) =int_a^bf(x) dx = F(b)...