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Integrals

Solve the improper integral

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

Application of Residues

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

Evaluate the Integrals

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

Integration and Simpson's Rule

(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

Evaluate integrals

(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,

Triple integral problem 9B

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

Double Integral : Volume of a solid - polar and rectangular coordinates

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

Integration: volume of solid

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).

Convergence Tests

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

Explanation to Convergence Tests

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

Integrals For Surface Area

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.

Problems

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] ---

Integration, volume of solid of revolution

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.

Integration

Let R be the region bounded by the curves: f(x) =ln(x+3) + 2 and g(x) = x^2 -8x + 18 Find the area of R. Show all work including integrals used and limits of integrations.

Integral calculus

Solve the given integral using integration by parts method. Integrate ∫x^2e^(3x) dx

Applications of integration

Let R be the shaded region bounded by the graphs of y=sqaure root of x, and y=e to the power of -3x, and the vertical line x=1. a) Find the area R b) Find the volume of the solid generated when R is revolved about the horizontal line y=1. c) The region R is the base of a solid. For this solid, each cross section perp

Double integrals problem

Would you please give me a detailed solution to the attached problem? 2) Let R be the region bounded by the graphs of y = x - sin x, y = π, and x = 0 a) Sketch the region R. b) Use a double integral to calculate the area of the region R.

One dimentional unsteady diffusion

(See attached file for full problem description) 5.7 a) Consider one-dimensional unsteady diffusion in an absorbing medium. The causal fundamental solution E with pole at x = 0, t=0 satisfies Reduce the problem to ordinary diffusion by the transformation E = b) What would be the significance of the problem in which q^2

Volume of a Solid of Revolution by Shell Method

Approximate the volume of the solid generated by revolving region formed by the curve y=x^2, x-axis and the line x=2. Volume approximated by concentric shells a) Sketch the reqion y=x^2, x-axis and the line x=2. b) We'll approximate the volume revolving the region about the y-axis. c) partition the interval [0, 2) in x,