### 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

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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

Evaluate the integral from 0 to infinity of (sin (xy))^2 / x^2 dx

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.

(x^2 + 3y^2) dx - 2xydy = 0 Integrate the differential equation. Complete step by step work must be shown and reduced into lowest terms.

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

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

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

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?

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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.

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).

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).

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

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.

L[y](x)= Integral between 0 and 1 (x-t)^2 y dt is a linear operator. or See attachment...

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)

Problem attached.

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

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

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

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.

Find the area of the region {(x, y)|0 <_ y <_ x^3 − 12x + 6, 4 <_ x <_ 6} <_ is to be taken as less then or equal to

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

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

Solve the differential equation. (x^2+1)dy/dx + xy = x