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    Integrals

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    Heat transfer and Heat Equations

    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

    Integration using trigonometric substitutions evaluated

    Please evaluate the following integral using trigonometric substitution. Please show each step in the solution. Then evaluate the answer for the limits 0 less than or equal to t less than or equal to ln4 ________ Integral e^t dt/ _/(e^2t +9)

    Triple integral convergence

    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?

    Integral : Average Value of a Function

    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.

    Solve: Integration using Trigonometric Substitution

    Please evaluate the following integral using trigonometric substitution. Please show each step in the solution. Then evaluate the answer for the limits 0 </= x </=1 &#8747;dx/(4-x²)³&#8242;² Integral dx/(4-x^2)^(3/2)

    Integrals : Time Needed to Pump Out a Tank

    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!

    Integrals : Volume of A Solid of Revolution Region

    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.

    Integration Using a Trigonometric Formula : ∫√(1-cos2x)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&#8804;x&#8804;pi Please show each step in the problem. Thank you. ∫√(1-cos2x)dx

    Integration by Trigonometric Substitution

    Please evaluate the following integral using basic formulas. Rewrite the integral to match it to a standard formula, and then solve the integral. Please show each step in the problem. Thank you. &#8747;dr/r&#8730;(r²-9)

    Viscous Fluid Flow : Viscous Drag on the Walls of a Pipe

    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

    Integration problems

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