### Integral Equation

Solve the integral equation: y(x) = 1 + integral from 0 to x of ( y(t)*t^2 dt) (in the integral is y as a function of t times t^2)

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Solve the integral equation: y(x) = 1 + integral from 0 to x of ( y(t)*t^2 dt) (in the integral is y as a function of t times t^2)

Derive the response of a viciously damped single-degree-of-freedom system of force Ft=F0e^-αt u(t) by means of a convolution integral. Plot the the response for the system parameters m=12 kg, c= 24 N.s/m, k=4.800 N/m and the force paramters F0=200 N, α=1 Prescribed Textbook: Fundamentals of vibrations : Leonard

Derive the response of a viciously damped single-degree-of-freedom system of force Ft=F0e^-αt u(t) by means of a convolution integral. Plot the the response for the system parameters m=12 kg, c= 24 N.s/m, k=4.800 N/m and the force paramters F0=200 N, α=1 Prescribed Textbook: Fundamentals of vibrations : Leonard

Please redo showing all steps.

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Please evaluate the following integral and show all steps in the solution. ∫x² / √(9-4x) dx integrate

3-3. Use the methods of vector calculus to derive the general heat conduction equation (Hint: Apply the first law to a volume V with surface S. and use the Gauss divergence theorem to Convert the surface integral of heat flow across S to a volume integral over V.) The cylindrical and spherical coordinate systems are examples o

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Hello. I'm trying to show if the triple integral: (z^2)/[(x^2+y^2+z^2)^(3/2)] dV converges or diverges over the region: x^2 + y^2 + z^2 <= 1. And if it converges, to what value? I am curious as to how I would do this, and how does one generally show if an integral converges or diverges? Thanks

Find the indefinite integral: (x+1/x)^2 dx

(See attached file for full problem description) Please follow instructions and show every last step please!

Find the numbers b such that the average value of f(x) = 2 + 6x - 3x^2 on the interval [0, b] is equal to 3. I know that fave = (1/b-a) (integral sign, b,a) f(x) dx , but I can't figure out how to isolate the b in that equation to find the unknown b.

A vertical right circular cylindrical tank measures 26 ft high and 10 ft in diameter. it is full of oil weighing 60 lbs/ft^3. How long will it take a 1/2 horsepower pump, rated at 275 ft x lbs/sec to pump the oil to the level of the top of the tank? Give your answer to the nearest minute!

Find the volume of the solid generated by revolving the region about the given line: the region in the first quadrant bounded above by the line y=2, below by the line y= (2x/5), and on the left by the y-axis, about the line y=2.

(See attached file for full problem description)

Rewrite the integral to match it to a standard formula, and then solve the integral. ∫x²/(x² + 1) dx

Please evaluate the following integral using basic formulas. Rewrite the integral to match it to a standard formula, and then solve the integral. Then evaluate the answer for the values 0≤x≤pi Please show each step in the problem. Thank you. ∫√(1-cos2x)dx

For laminar flow in the entrance of to a pipe, as shown in figure, the entrance is uniform u=U0, and the flow downstream is parabolic in profileu(r)=C(r0^2-r^2). Using integrla relations, show that the viscous drag exerted on the pipe walls between 0 and x is... Prescribed text book: White, FM, , Viscous Fluid Flow, 2nd Editi

Please evaluate the following integral using trigonometric substitution. Consider: Integral (9-w^2)dw/ w^2

Please help me evaluate the following integral using trigonometric substitution. Please show all steps involved. thank you. The problem is: ∫3dy/ √(1 + 9y²)

See attached file for full problem description.

Can you please provide a detailed explanation of how to evaluate these questions? (See attached file for full problem description)

Question 1: What is the exact value of ∫ 0-->2 x^3 + 3x^2 dx ? Question 2: Find SIMP(n) for n = 2, 4, 100. What is noticeable? ---

Please see the attachment for the questions.

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Calculate the integral. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). Please see the attached file for the fully formatted problem. integrate, integration