### Proof : Show integral is zero.

If Xc is the function from to such that Xc(x)={1 if x=c and cE[a,b] , show that ∫a-->b Xc =0. {0 if x≠c Please see the attached file for the fully formatted problems.

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

If Xc is the function from to such that Xc(x)={1 if x=c and cE[a,b] , show that ∫a-->b Xc =0. {0 if x≠c Please see the attached file for the fully formatted problems.

If and are functions from to which are Riemann integrable on and which differ at only a finite number of points in , show that . Please see the attached file for the fully formatted problems.

Consider the nonlinear Fredholm equation where is continuous on [a,b] and is continuous and satisfies a Lipschitz condition: on the set . Show that the integral equation has a unique solution on [a,b] if .

4 A) Evaluate ∫ 6x(2x^2 - 1) dx 2 b) Write down a definite integral that will give the value of the area under the curve y=x^3 cos (1/4 x) between x=pi and x=2pi pi=3.142 (you are not asked to evaluate the integral by hand) c) use mathcad to find the area described in par

Find the indefinite integral of the following function. g(x)= 19+15^3/x

(See attached file for full problem description)

(See attached file for full problem description) Assume that f is continuous on Reals and periodic with p. Show that for any a

Find the indefinate integrals off the following functions: f(t) = 2cos(4t) - 3e^5t g(x) = (19+15x^3)/ x (x>0) h(u)= sin^2[(1/10)u] I'm struggling to understand these questions so if someone could write a/n solution/explanation for them that would be great.

(See attached file for full problem description) --- Assume that f is continuous on [a,b] and f(x) 0 for each x [a,b]. Prove that >0 if there exists c (a,b) such that f(c)>0.

1. The United States Census Bureau mid-year data for the population of the world in the year 2000 was 6.079 billion. Three years later, in 2003, it was 6.302 billion. Answer the following questions. (See attached bmp file) 2. A metal ball, initially at a temperature of 90 C, is immersed on a large body of water at a temperat

(See attached file for full problem description with proper equations) Evaluate these: 1. Find dw/dx for the function given by w=xye^(xyz) 2. Find the center and radius of the sphere given by the equation x^2 + y^2 + z^2 + 4x - 2y + 2z=10 3. The sum of $2000 is deposited in a savings account earning r percent int

Integrate: cos^2 theta. keywords: integration, integrates, integrals, integrating, double, triple, multiple, trig

Application of Residue theorem. See attached file for full problem description.

Create an integral whereby you are forced to use all four types of integration. Work the problem and explain why each (u-substitution, trig substitution, fractions, parts) are all needed. this must be only one integral, that is it must all be under a singular fraction and cannot be the sum such as integral of lnx+arctanx dx or

Please provide in-depth evaluation of improper integrals using residues theorem.

(See attached file for full problem description) I tried solve this problem by following Cauchy's Residue Theorem. However, the answer is always wrong.

I want to find the Cauchy value by using residues. (See attached file for full problem description)

A. Evaluate ∫ x(sqrt(x+1))dx B. Find the area bounded by y= x/(1+x)^2, y=0, x=0, and x=2 C. Evaluate ∫ 1/x(sqrt(x+9))dx D. Find the indefinite integral using integration by parts: ∫x^2(e^2x)dx Infinity Evaluate the improper integral: ∫ ln(x)dx

(See attached file for full problem description with proper symbols and equations) --- A. Evaluate the improper integral: Infinity ∫ (xe^x^2)dx 0 B. Complete the square, then use integration tables to evaluate the indefinite integral: ∫ {(sqrt(x^2 + 6x + 13))/x+3}dx C. Which of the followin

(See attached file for full problem description with proper questions) 1. Find the indefinite integral 2. Find the definite integral:(4x+1)1/2 dx 3. Find the area of region bound by the graphs of the equations, then use a graphing utility to graph the region and verify your answer: Y=x(x-2)^(1/3) Y=0,

Let Q be the sphere: X^2 + Y^2 + Z^2 = a^2 a) Use CYLINDRICAL coordinates to set up the integral to calculate the volume of Q b) Use SPHERICAL coordinates to set up the integral to calculate the volume of Q c) Solve for Q using either a or b

Consider the solid bounded above by the plane Z = 4 and below by the circle X^2 + Y^2 = 16 in the XY-plane. a) Write the double integral in rectangular coordinates to calculate the volume of the solid. b) Write the double integral in polar coordinates to calculate the volume of the solid. c) Evaluate part a or part b

Let f and g be the functions given by f(x) = 1 + sin(2x) and g(x) = e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x).

Using one of the tests for convergence (ratio, root, comparison, limit, integral, nth term, etc.), show whether the following series converges or diverges: ∞ ∑ n(2^n)(n + 1)! / (3^n)n! n=1

Using one of the tests for convergence (comparison, limit, integral, nth term, etc.), show whether the following series converges or diverges: infinity E (1 + cos n)/ n^2 n=1

Use the integrating capabilities of a graphing utility to approximate the surface area of that portion of the surface z=e^x that lies over the region in the xy-plane bounded by the graphs of y=0, y=x and x=1. Round answer to three decimal places.

1. Find the definite integral. ∫0-->1 (e^-x)/(e-x + 1)^1/2 (The interval is [0, 1]) integrate, integration

1. Find the definite integral. 0/1 (e^-x)/(e-x + 1)^1/2 2. use the midpoint rule with n=4 to approximate the area of the region bounded by the graph of f and x-axis over the interval. Compare your result with the exact area. Sketch the region a. f(x)=x^2(3-x) [0,3] b. f(x)=x^2 - x^3 [-1, 0] ---

Evaluate the integral: 1 1 S S sin(x^2) dx dy 0 y

Let R be the region bounded by the curves f(x) = ln(x+3) +2 and g(x) = x^2 - 8x + 18. a) Using the washer method, find the volume of the shape which is formed if R is rotated around the x- axis. b) Using the cylindrical shells method, find the volume of the shape which is formed is R is rotated around the line x = -2.