Integration Cubed Root Functions
Please see the attached file for full problem description. Integrate the following
Please see the attached file for full problem description. Integrate the following
Using: d tan^-1 (x/y)=(y dx - x dy)/(x^2 + y^2), and ½ d ln(x^2 + y^2)=(x dx + y dy)/(x^2 + y^2) find integrating factors for, and solve, the following equation: (2x^(2)y + 2y^3 - x) (dy/dx) + y=0
Laplace Transform Application of Complex Inversion Integral Formula (Bromwich's Integral Formula) Problem:- Find the Laplace Transform of the function F(t) = (1 - e^(
See word file for problems regarding the ladder method of integration by parts
Show that (7x/x^2 + 5) + (4/3x+15) - (5/6x-24) = (45x^3-15x^2-825x-35)/((6x^2+30)(x^2+x-20)) then use that information to determine S=integral S(45x^3-15x^2-825x-35)/((6x^2+30)(x^2+x-20)) dx.
Please see the attached file for the fully formatted problems. Partial fraction decomposition is a technique used to convert a fraction with a polynomial numerator and a polynomial denominator into the sum of two or more simpler fractions. It eases integration by reducing it to the sum of integrals, each of which will most l
1. The shaded region R, is bounded by the graph of y = x^2 and the line y = 4. a) Find the area of R. b) Find the volume of the solid generated by revolving R about the x-axis. c) There exists a number k, k>4, such that when R is revolved about the line y = k, the resulting solid has the same volume as the solid in par
See attachment Integrate the following
Integrate the following: y = (x - x^2)/(x^(1/6))
Please see the attached file for the fully formatted problem. Integrate the following I have finished with What happens with the 9.4? Am I right so far?
Laplace Transform Inverse Laplace Transform To find the integral of e^(-x^2) by using Laplace Transform, where the range of integration is from 0 to infinity.
Laplace Transform Application of Complex Inversion Integral Formula (Bromwich's Integral Formula) Problem:- Find the Laplace Transform of the function F(t) = (1 - e^(-at))/a
Use an iterated integral to find the area of the region: y = 1 /sq root (x - 1)
Please see the attached file for the fully formatted problem. Use the indicated change of variables to evaluate the double integral: SR S 60xy dA x = 1/2(u + v) y = -1/2(u - v)
Find the indefinite integral (3-x)/sq root of 9-x^2 dx(dx would be in the numerator). I tried to split this problem apart. First part was: The integral of 3/sq root of 9-x^2 dx and found 3 arcsin x/3 + C, then Second part was: The integral of -x/sq root of 9-x^2 dx and found -3/4 -x + C. I then put them back together to ge
Note: If you have already answered this exact question please do not answer it again. I would like an answer from a different T.A. Thanks Say abs = absolute value. Suppose that the function f:[a,b]->R is Lipschitz; that is , there is a number c such that: abs(f(u) - f(v)) <= (c)abs(u-v) for all u and v in [a,b]. Let P
For numbers a1,....,an, define p(x) = a1x +a2x^2+....+anx^n for all x. Suppose that: (a1)/2 + (a2)/3 +....+ (an)/(n+1) = 0 Prove that there is some point x in the interval (0,1) such that p(x) = 0
Please see the attached file for the fully formatted problems. Attached is a file with a three part successive approximation problem. The following problems are to use the method of successive approximations (Picard's) [EQUATION] y x y fty tdt =+∫n− with a choice of initial approximation other than y0(x)=y0
Use the given information: the functions g:[a,b]->R and h:[a,b]->R are continuous with h(x) >= 0 for all x in [a,b], and there is a point c in (a,b) such that: the integral from a to b of h(x)g(x)dx = g(c) times the integral from a to b of h(x)dx. to show that the Cauchy Integral Remainder Theorem implies the Lagrang
Apply Green's Theorem to evaluate the integral over C of 2(x^2+y^2)dx + (x+y)^2 dy, where C is the boundary of the triangle with vertices (1,1), (2,2) and (1,3) oriented in the counterclockwise direction. Also check the result by direct integration. Please show detailed working so I can follow the steps of the working.
Find the indefinite integrals (anti-derivatives): Find the indefinite integrals (anti-derivatives): a.) x / (x +2) dx I found ½ ln + + C as an answer - is this correct? b.) 1 / (x +2) dx I found 1/x arctan /x + C as an answer - is this correct? (I said that a = x, u = , du = dx )
Let f: [a,b] be mapped onto the Reals be a function that is integrable over [a,b] and let g: [a,b] be mapped onto the Reals be a function that agrees with f except at finitely many points. Is g integrable over [a,b]? Why or why not?
Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].
Please see the attached file for the fully formatted problems. I.A. Sketch the following region in the x-y plane: R: 0<x<b^2 : x^1/2 < y< b B. Set up integral R for (e^-y2)/y dA in two ways.
Please see the attached file for the fully formatted problems. Set up triple integral for volume of cone, do not evaluate.
Please see the attached file for the fully formatted problems. Sketch the curve r = 5 - 3cos(theta) and set up double integral for bounded area in the third quadrant.
Evaluate the following indefinite integral. int[(x^a)sqrt(r+tx^(a+1))]dx, (t not=0, a not=-1). (See attachment)
Use residues to evaluate this improper integral Int(from 0 to inf)[cos(ax)/(x^2+1)]dx (a>0) (See attachment for better description.)
1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2) 2) Find the volume of the solid bounded above and below by the cone (z^2) = (x^2) + (y^2), and the side by y=0 and y= square root(4-(x^2)-(z^2))
Suppose that the functions g:[a,b]-> R are continuous. Prove that: The integral from a to b of gf <= (the square root of the integral from a to b of g^2) multiplied by (the square root from a to b of f^2)