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  • Math
    `int (x+2)/(x^2+5x) dx` To solve using partial fraction method, the denominator of the integrand should be factored. `(x+2)/(x^2+5x) = (x + 2)/(x(x+5))` Then, express it as sum of fractions....

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(2x^3-4x^2-15x+5)/(x^2-2x-8)dx` The integrand is a improper rational function,as the degree of the numerator is greater than the degree of the denominator.So we have to carry out division....

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(x^3-x+3)/(x^2+x-2)dx` The given integrand is a improper rational function, as the degree of the numerator is more than the degree of the denominator. To apply the method of partial...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (x^2+12x+12)/(x^3-4x)dx ` To solve using partial fraction method, the denominator of the integrand should be factored. `(x^2+12x+12)/(x^3-4x) =(x^2+12x+12)/(x(x-2)(x+2))` Then, express it as...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(3-x)/(3x^2-2x-1)dx` Let's use partial fraction decomposition on the integrand, `(3-x)/(3x^2-2x-1)=(3-x)/(3x^2+x-3x-1)` `=(3-x)/(x(3x+1)-1(3x+1))` `=(3-x)/((3x+1)(x-1))` Now form the partial...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int 5/(x^2+3x-4)dx` To solve using partial fraction, the denominator of the integrand should be factored. `5/(x^2+3x-4)=5/((x+4)(x-1))` Then, express it as sum of fractions....

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int 2/(9x^2-1)` To solve using partial fraction method, the denominator of the integrand should be factored. `2/(9x^2-1) = 2/((3x-1)(3x+1))` Then, express it as sum of fractions....

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int 1/(x^2-9)dx` To solve using the partial fraction method, the first step is to factor the denominator of the integrand. `1/(x^2-9) =1/((x - 3)(x +3))` Then, express it as a sum of two...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To find the arc length of a curve, we follow the formula: `S = int_a^b sqrt(1+((dy)/(dx))^2)` if `y=f(x)` , `alt=xlt=b` or ` [a,b]` . For the given problem: `y =x^2/2` on interval `[0,4]` , we...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Arc length of curve can be denoted as "`S` ". We can determine it by using integral formula on a closed interval [a,b] as: `S = int_a^b ds` where: `ds = sqrt(1+ ((dy)/(dx))^2 )dx` ` if y=f(x)`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Volume of a shape bounded by curve `y=f(x)` and `x`-axis between `a leq x leq b` revolving about `y`-axis is given by `V_y=2pi int_a^b xy dx` In order to use the above formula we first need to...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To find the volume of the torus generated by revolving the region bounded by the graph of circle about the y-axis, we may apply Washer method. In this method, rectangular strip representation that...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intx/sqrt(x^2-6x+5)dx` Let's complete the square of the denominator of the integrand, `=intx/sqrt((x-3)^2-4)dx` Now apply integral substitution:`u=x-3` `=>du=1dx` `=int(u+3)/sqrt(u^2-2^2)du`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall indefinite integral follows `int f(x) dx = F(x)+C` where: `f(x)` as the integrand `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. To evaluate the given integral:...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration.. To evaluate the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int1/sqrt(4x-x^2)dx` Complete the square for the denominator of the integrand, `=int1/sqrt(-(x-2)^2+4)dx` Now apply integral substitution:`u=x-2` `=>du=1dx` `=int1/sqrt(-u^2+4)du`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. The given integral...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. The given...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Indefinite integral are written in the form of `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the anti-derivative function of `f(x)` `C ` as the arbitrary...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int1/(4+4x^2+x^4)dx` Let's rewrite the integrand as : `=int1/((x^2)^2+2(2)(x^2)+2^2)dx` `=int1/(x^2+2)^2dx` Apply integral substitution:`x=sqrt(2)tan(u),u=arctan(x/sqrt(2))` `dx=sqrt(2)sec^2(u)du`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given, `int sqrt(1-x)/sqrt(x) dx` let us consider `u= sqrt(x)` , we can write it as `u^2 = x` Differentiating on both sides we get => `(2u)du = dx` Now let us solve the integral , `int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the anti-derivative function `C` as the arbitrary...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the anti-derivative function `C` as the arbitrary...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(-3x)/(x^2+3)^(3/2)dx` Take the constant out, `=-3intx/(x^2+3)^(3/2)dx` Apply integral substitution:`u=x^2+3` `=>du=2xdx` `=-3int1/(u)^(3/2)(du)/2` Take the constant out,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the anti-derivative function `C` as the arbitrary...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Indefinite integral are written in the form of `int f(x) dx = F(x) +C` where: `f(x)` as the integrand `F(x)` as the anti-derivative function `C` as the arbitrary constant...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To solve the indefinite integral, we follow `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. For the given...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given , `int sqrt(1-x^2)/x^4 dx` By applying Integration by parts we can solve the given integral so, let `u= sqrt(1-x^2)` `,v' = (1/x^4) ` =>` u' = (sqrt(1-x^2) )'` => =`d/dx (sqrt(1-x^2))...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int1/sqrt(x^2-4)dx` Let's apply integral substitution:`x=2sec(u)` `=>dx=2sec(u)tan(u)du` `=int1/sqrt((2sec(u))^2-4)2sec(u)tan(u)du` `=int(2sec(u)tan(u))/sqrt(4sec^2(u)-4)du`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given , `int sqrt(16-4x^2)dx` This Integral can be solved by using the Trigonometric substitutions (Trig substitutions) For `sqrt(a-bx^2)` we have to take `x=` `sqrt(a/b) sin(u)` so here , For...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given `int x^2/sqrt(36-x^2) dx` This can be solved by using the Trigonometric substitutions (Trig substitutions) when the integral contains `sqrt(a-bx^2)` then we have to take `x=sqrt(a/b) sin(t)`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given to solve , `int 1/sqrt(16-x^2) dx` using the Trig substitutions for `sqrt(a-bx^2)` `x= sqrt(a/b) sin(u)` so for , `int 1/sqrt(16-x^2) dx` --------(1) so , `x` can be `x= sqrt(16/1) sin(u)` =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that indefinite integral follows the formula: `int f(x) dx = F(x) +C` where:` f(x)` as the integrand `F(x)` as the anti-derivative function `C` as the arbitrary...

    Asked by enotes on via web

    1 educator answer.

  • Math
    given to solve , `int sqrt(25-x^2) dx` using the Trig Substitutions we can solve these type of integrals easily and the solution is as follows for `sqrt(a-bx^2) ` we can take `x= sqrt(a/b)...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given to solve, `int sqrt(4+x^2) dx` using the Trig Substitutions we can solve these type of integrals easily and the solution is as follows for `sqrt(a+bx^2) ` we can take `x= sqrt(a/b)...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Given to solve, `int sqrt(9+16x^2) dx` by using the trig substitution , we can solve the integral for `sqrt(a +bx^2)` ` dx ` the `x` is given as `x= sqrt(a/b) tan(u)` so, for the integral `int...

    Asked by enotes on via web

    1 educator answer.

  • History
    When we use the term "Renaissance Man" today, we still first think of Leonardo da Vinci as the epitome of the moniker, though he lived over 500 years ago. Da Vinci created new techniques in...

    Asked by user7120018 on via web

    1 educator answer.

  • History
    Sectionalism arose in the United States as a response to the differences in the economies of the different regions of the United States. The North, which did not enjoy the fertile lands of the...

    Asked by ikoradia on via web

    1 educator answer.

  • Rikki-Tikki-Tavi
    A cantonment is a military base in India. The Kipling Society notes that the Segowlee Cantonment is a fictitious location; however, a cantonment is a real place where soldiers live and train. A...

    Asked by user4248341 on via web

    1 educator answer.

  • The Scarlet Letter
    Hester's daughter, Pearl, needs her father to acknowledge her. Until he does, she exists only as a symbol: of her parents' love, their sin, their secret, her father's guilt, her mother's scarlet...

    Asked by lottiemartekah on via web

    1 educator answer.

  • Le Morte d'Arthur
    To ascertain the difference between "good" and "bad" knights in Le Morte D'Arthur, we must look at the standard knights were measured by during Arthur's time. This standard is referred to as the...

    Asked by happyangel4real on via web

    1 educator answer.

  • Hoot
    Roy was born in Detroit, Michigan, but the family had moved away from there when he was just a baby, so he couldn't remember anything about Detroit. He didn't think of it as his hometown since he...

    Asked by dalonso06 on via web

    1 educator answer.

  • Law and Politics
    The answer to this is “absolutely not.” A constitution is just a piece of paper. It can only be enforced on the government if the people are willing to do so. This means the government does...

    Asked by user5484233 on via web

    1 educator answer.

  • The Secret Life of Walter Mitty
    In Walter's last daydream, he defiantly faces a firing squad, confident in his ability to die courageously. He scornfully rejects the handkerchief or blindfold, preferring to face his fate with...

    Asked by user1377635 on via web

    1 educator answer.

  • The Possibility of Evil
    To find examples of Miss Strangeworth being evil, look towards the end of the story when she is composing her next round of poison pen letters. Miss Strangeworth shows her darker side, for...

    Asked by user9489820 on via web

    1 educator answer.

  • History
    The rise of Christianity in Europe during the Middle Ages led to changing views of the human body. Christianity, and more specifically Catholicism, emphasized modesty and chastity. Most artistic...

    Asked by ellenaludtke on via web

    1 educator answer.

  • The Sun Also Rises
    This question has been answered: http://www.enotes.com/homework-help/hemingways-sun-also-rises-what-elements-realism-709283#answer-751067

    Asked by user4937930 on via web

  • Ozymandias
    Shelley wrote "Ozymandias" for several reasons. First, the poem was inspired by the arrival in England of a portion of a statue of the ancient Egyptian pharaoh Ramesses II. Shelley wanted to...

    Asked by user5736343 on via web

    1 educator answer.

  • History
    The world experienced two Industrial Revolutions. The first one occurred in the mid-1700s and lasted until the mid-1800s. The Second Industrial Revolution occurred from around 1870 until the...

    Asked by marcmtz3 on via web

    1 educator answer.

  • History
    Both the Great Awakening and the Enlightenment were eighteenth-century movements. They were both influential throughout the British Atlantic, including Great Britain's North American colonies. They...

    Asked by zisbello on via web

    1 educator answer.

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