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    Integrals

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    Solving for a Line Integral

    Show that the line integral is independent of the path and evaluate the integral: Integral_c (2xsinydx) + (x^2cosy - 3y^2)dy C is any path from (-1, 0) to (5,1).

    Line integral evaluation directly and by Green's Thorem

    See attached page for problem. Evaluate the line integral by two methods, directly and Green's Theorem integral_c (x + 2y)dx + (x-2y)dy C consists of the arc of the parabola y=x^2 from (0, 0) to (1, 1) followed by the line segment from (1, 1) to (0, 0)

    Green's Theorem Used to Evaluate Integrals

    Use Green's Theorem to evaluate the line integral along the given positively oriented curve. Below, 'S' represents the integral sign. 1) S_c xy dx + y^5 dy C is the triangle with verticies (0,0), (2,0) and (2,1). 2) S_c (y + e^sqrt(x) )dx + (2x + cos(y^2) ) dy C is bounded by the region enclosed by parabolas y = x

    Asymptotic expansion

    File attached. Please show all work. Thanks Using integration by parts find the first 3 terms of the asymptotic expansion

    Integral test of series

    Determine whether the series is convergent or divergent. 1 + 1/(2*sqrt[2]) + 1/(3*sqrt[3]) + 1/(4*sqrt[4]) + 1/(5*sqrt[5]) + ... Please show steps.

    Line integral

    Pleas see the attached page for problems. Evaluate the line integral, where C is the given curve

    Ellipse integral

    See attached page for problem. Use the given transformation to evaluate the integral.

    How do you calculate the area enclosed between curves?

    Please see the attached file for the three problems. Question 16: Give the are of the region bounded by the graphs of R(x) = -x^2 + 6 G(x) = x and the vertical line x = 3. Question 17: Give the area of the region bounded by the graphs of R(x) = -x^2 + 3 G(x) = -2x and the vertical line x = -2. Question 18:

    What is the area enclosed between the two curves?

    Please see the attached file for three problems on area enclosed between curves. Question 13: Give the area of the region bounded by the graphs of G(x) = x^2 - 8 F(x) = 2x and the vertical line x = -3. Question 14: Give the area of the region bounded by the graphs of H(x) = x^2 - 10 Q(x) = 3x and the ver

    Computing for the Integral

    Compute the following: 1. Integral(pi - 0) (-2cos (x) - 2sin (x)) dx a. -5 b. -4 c. -2 d. -6 e. 4 f. None of the above. 2. Integral(1 - 0) (-x + 3)^2 dx a. (16/3) b. (41/6) c. (35/6) d. (22/3) e. (19/3) f. None of the above. 3. Integral((1/6)pi - 0) (-cos (3x) dx) a. 1/6 b. -1/3 c. 2/3 d. -5/6 e

    Polynomial equations and integrating area under curve

    I need to find the area of each with respect to the x axis I have the following 2 polynomial equations: (1) y = -24.034x^4 + 440.02x^3 - 2814.5x^2 + 7050.2x - 4660 y values range from 0 to 1275 and x values range from 0 to 6 (2) y = -721.34x^5 + 15484x^4 - 123523x^3 + 443283x^2 - 678627x + 396008 y values range fr

    Application of Derivative and Evalution of Integral

    1. find dx/dt of x= sqrt(1+cot(3t)). 2. f(x)=(x-2)^2*(x+3)^2, find the interval on which the function f(x) is increasing and decreasing. sketch the graph of y=f(x), and identify and local maximum or mininmum and golobal extrema. 3. f(x)= x^2/(x-1) sketch the graph, identify all extrema, inflection points, intercepts, and a

    An example of contour integration using Cauchy's formula

    Evaluate the contour integral of z^2/(4-z^2) around the circle |z+1|=2. The question is attached in correct mathematical notation, along with the student's (incorrect) initial attempt. You will need to refer to this initial attempt when reading the solution.

    Inverse trigonometric functions, L'Hopitals Rule and Integration by Parts

    Please see the attached file for the fully formatted problems. 1. Prove that d/dx (csc^-1 x) = - (1 / x(square root x^2 - 1) 2. Find the derivative of the function. Simplify where possible. y = tan^-1 (x/Q) + ln (square root (x-Q)/(x+Q)) 3. Find the limit using l'Hopital's Rule where appropriate. If there is a more e

    Area between graphs

    For the functions: f(x)=4-x^2 g(x)=e^(-x) a. Sketch both graphs. Find and label the intersection points. b. Find the area between the graphs using integration. Give the full integral, including limits, in proper notation.

    An example using Cauchy's theorem

    Let f be entire. Evaluate the integral from zero to 2 pi of f(z_0+re^(i theta)) e^(ik theta), where z_0 is a constant and k is a constant greater than or equal to 1.

    Trigonometry: Solving Integrals

    Please solve the following integral: 1) Determine the integral sin^3(3x)cos^6(3x)dx Make sure to show all of the steps which are required.

    Integration Determination

    4A) Determine the integral x /(square root of x^2+4) dx by u substitution. 4B) Determine the integral dx /(square root of x^2+4) 4C) Determine the integral dx / x^2+4

    Solve: Integration by Substitution

    It is essential to show all steps by hand. Also if a method is prescribed, use only that method. Keeping this involved, solve the following: 1A) Determine the integral dx/x^2+12x+36 by using substitution. 1B) Determine the integral dx/x^2+12x+40.