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Integrals

Integration using trigonometric substitutions

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)

Convergence of Integrals

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

Surface Areas of Revolution

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

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.

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!

Integration Using a Trigonometric Formula : &#8747;&#8730;(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. &#8747;&#8730;(1-cos2x)dx

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)

Simpson's Rule

Question 1: What is the exact value of &#8747; 0-->2 x^3 + 3x^2 dx ? Question 2: Find SIMP(n) for n = 2, 4, 100. What is noticeable? ---

Integration by parts

Please evaluate the following integral using the formula for integration by parts, int (udv) = uv - int (vdu) Int z(ln z)²dz

Evaluate the Integral : &#8747;1/(4-z^2)^3/2 dz

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

Complete explanation of integration problems

Solve. Show all the steps. 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). integral (1/(cos^4)7x)dx

Integration by parts

In this problem I am asked to use integration by parts utilizing the formula: &#8747;udv = uv - &#8747;vdu Please show the values of u, dv, du, and v and the steps to achieve the solution. Thank you. &#8747;x²sinx dx

Surface Area of a Revolving Curve

Using the formula for the surface area of a revolving curve about the y-axis: S=&#8747;2&#960;x&#8730;(1 + (dx/dy)²)dy throughout a,b Find the area of the surface generated by revolving the curve about the y axis within the given boundaries x=&#8730;(2y-1) 5/8&#8804;y&#8804;1 the revolving base passes thr

Surface Area of a Revolved Curve

Utilise the following formula that gives the surface area of a curve that revolves around the y-axis: S=&#8747;2&#960;x&#8730;(1 + (dx/dy)²)dy throughout c, d Now calculate the area of the surface that would come about by rotating the curve around the y axis with the boundaries below: x = (1/3)y³&#8242;² - y ¹&#824

Area between two curves

The area I am looking for is the region bounded by the two functions y=x² and y=2-x between the limits (2,0) and (0,0) and bounded by the x axis and the point y=1 What is the area between these two curves? Using the formula A=&#8747;f(x)-g(x)dx

Riemann Sum Area Between Two Curves

Using the Riemann sum formula: A = &#8747; [f(x) - g(x)]dx from a to b Find the area between y=1/2sec²t and y= -4sin²t between the points &#960;&#8725;3 and - &#960;&#8725;3 Please show a detailed solution. Thank you.