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Integrals

Integration

Find the volume of the solid obtained by rotating the region bounded by the given curves: y=1/x^6, y=0, x=4, x=8 about the "y" axis

Integrals

Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by: y= x^4 y= 125x about the x-axis. I am more concerned with understanding than the answer. Thanks for your help.

Integration

If f(x) = int_{1}^{x^{2}} t^2dt then f'(x)= then f'(5)=

Evaluate the integral

The following expression describes the total electric current to pass in the circuit please see attached

Integration

Decide whether to integrate with respect to "X" and "Y", then find the area of the region. x+y^2=42, x+y=0.

Integral domain

There is integral domain with exactly six elements. Disprove or Prove

MATLAB Programming

Develop a program (M-File) called 'integrate' that will perform a first-order numerical approximation, yi(t), of the running integral with respect to time of an array of experimental data y(t). The M-File must also perform another first order approximation, yi2(t), of the first integral resulting in a double integration of the

Differential Equations

Please see the attached file for the fully formatted problems. y(t) + S t-->0 (t-tau)y(tau) dtau = e^t

Integrals

Determine the indefinite integral: z = (Integral Sign or "Long S")20xe^-4x dx. I got z = 5xe^-4x + 5/4 e^-4x + C - Does that seem right?

Simpson's Rule

Find the integral of e^-x dx from x = 0 to 1 with Simpson's rule using 10 strips.

Evaluate the Surface Integral

Please see the attached file for the fully formatted problems. Evaluate the surface integral SSs x dS, where S is part of the plane x = 2y = 3z = 6 that lies in the first octant.

Green's Theorem : Evaluating a Line Integral

Please see the attached file for the fully formatted problems. Use Green's Theorem to evaluate the line integral Sc xy dx +x^2y^3 dy where C is the triangle with vertices (0,0), (2,0) and (2,2).

Gradients : Find a Function and Evaluate an Integral

Please see the attached file for the fully formatted problems. (a) Find a function f so that grad(f) = yi + (x + 3y^2)j (b) Use part (a) to evaluate Sc grad(f) dt where C is the path starting at (0,2) goes down the y-axis to (0,0), along the x-axis to (2,0).

Iterated Integral

Please see the attached file for the fully formatted problems. Evaluate the iterated integral S 1-->0 S z--> 0 S x+z --> 0 x dydxdz

Polar Coordinates

Please see the attached file for the fully formatted problem. By changing to polar coordinates, evaluate SSR (x+y) dA where R is the disk of radius 4 centered at the origin.

Integration

How do you integrate: [a^x exp(-a) ] / x ! (The ^ represents 'to the power of ' so a^x implies a raised to the power x)

Integration

I've included the problem as a JPEG . Thank you

Combinatorial Result about the Binomial Coefficients

Please see the attached PDF file for the fully formatted problem. By the Binomial Theorem .... Therefore .... Evaluate the integral to get .... by a similar line of reasoning. Since this is an analysis problem, please be sure to be rigorous, and include as much detail as possible so that I can understand. Please also

Evaluate an Integral

Please see the attached file for the fully formatted problems. Reverse the order of integration to evaluate S 2 ---> 0 S 1 ---> y/2 cos(x^2) dxdy

Compute the volume of a solid.

A solid has a rectangular base in the x,y-plane with sides parallel to the coordinate axes and with opposite comers at points (0,0) and (4,6). The solid's sides are vertical, and the top is determined by the plane z = 3x + y. Compute the volume of the solid.

Evaluating an Integral using Jordan's Lemma

The problem is: Evaluate the integral from 0 to INF of: [(x^(1/3))*(ln x)]/(x^2 +9) dx by using f(z)= [(z^(1/3))*(Log z)]/(z^2 +9), with -pi/2 < Log z < 3pi/2. Also, with z^(1/3)= e^[(1/3)Log z]. We are to use the curve C: from -R to -p, -p to p around origin, p to R, and Cr from 0 to pi. Many thanks in advance

Evaluating an Integral using Jordan's Lemma

The problem is to find the value of the integral from 0 to INF of [(ln x)^2]/(x^2 +9). We are to use f(z)= [(Log z)^2]/(z^2 +9), where -pi/2 < Log z < 3pi/2. We are to use the curve C from -R to -p along the real axis, -p to p around 0, p to R along the real axis, and the curve Cr from 0 to pi. I am having several probl