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.
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.
Solve the given integral by the method of partial fractions: (S stands for the integration sign) S sec^2(x) / (tan^3(x) - tan^2(x)) dx
Integrate the integral below using the partial fractions method. (S represents the sign for integration) S x^3 + 4 / (x^2 - 1)(x^2 + 3x + 2) dx
Solve the given integral using integration by parts method. Integrate ∫x^2e^(3x) dx
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
Please give me a detailed solution to the attached problem.
Please give a detailed answer to the attached problem.
Please give a detailed solution to the attached problem.
1 3 ∫ ∫ e^x dx dy 0 3y Would someone please give me a detailed solution to this 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.
I(a)=∫0-->pi/2 1/(1 + tan x)^a integrate, integration
(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
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,
∫x^2/√(25-x^2) To solve a given indefinite integral using a suitable trigonometric function substituted. Please see the attachment for the problem.
A lamina (with uniform thickness 0.01m) has the shape in the xy plane bounded by the curves y-4-x^2, y=0, If the density given is constant, find the centroid. Please see the attached file for the fully formatted problems. integrals, integrating
Applications of Integrals : Area of a region Bounded by Three Curves and Volumes of Solids of Revolution
Let R be the shaded region in the first quadrant enclosed by the graphs of y=e^(-x^2), y= 1-cos x, y-axis as shown in the figure above. (a) Find the area of the region R. (b) Find the volume of the solid generated when the region R is revolved about the x-axis. (c) The region R is the base of a solid. For this solid, each cr
Let R and S be regions in the first quadrant. R is bounded by the x-axis, y=2-x^3 and y=tan x. S is bounded by the y-axis, y=2-x^3 and y=tan x. a) Find area of R. b) Find area of S c) Find volume of the solid generated when S is revolved about the x-axis.
The problem is: ∫∫ y/x^2 + y^2 dA R R is the triangle bounded by y=x, y=2x, x=2
Integrating using the Midpoint Rule; Eliminating Parameters and Slope of Tangent at Y-axis Crossings
1.) Estimate integral from (0 to 2) of 1/(2+x^2) dx using the midpoint rule n=4 2.) Eliminate parameter of parmetric equation x=cos theta y= sin ^2 theta sketch the Cartesian graph equal to 0 less than or equal to theta less than or equal to sin pi/2 3.) x=
Compute the residues of the function 1/[(z^2+1)(z^2+4)] at each of its poles. Hence compute the real integral.
I have completed the answers to the questions. I just need to have someone confirm that they are correct. Thank you! True/False Indicate whether the sentence or statement is true or false. F 1. Management science is the application of a scientific approach to solving management problems in order to h
Minimization Problem : Find a,b,c Є R such that ∫-1-->1 |x^3-a-bx-cx^2|^2 dx is minimized.
Find a,b,c Є R such that ∫-1-->1 |x^3 - a -bx -cx^2|^2 dx is minimized.
Consider the system shown in Fig.1. (attached file) This is a PID control of a second-order plant G(s). Assume that disturbances D(s) enter the system as shown in the diagram. It is assumed that the reference input R(s) is normally held constant, and the response characteristics to disturbances are a very important consideration
Use partial decomposition to integrate (x-7)/(x^2-x-12 ) (5x)/(2x^3+6x^2 ) (x^3-8x^2-1)/(x+3)(x^2-4x+5)
Use partial decomposition to integrate. (2x^2-x-20)/(x^2+x-6 ) (sint)(4cos^2t-1)/(cost)(1+2cos^2t+cos^4t) (x+pi )/(x^2-3pix+2pi^2)
Work done by a particle as it moves along a curve (parabola); Integral of a region bounded by two lines.
Please see the attached file for the fully formatted problems.
∫(2-2Cos(2t))^(-3/2). integral, integration