The base of a particularly curvy building is described by [tex]y=x*sin(3x)+10[/tex] with [tex]y[/tex] in feet and [tex]x[/tex] is in tens of feet for [tex]0 \leq x \leq 3\pi[/tex]. Views are shown in the attached file i uploaded. The cross sections perpendicular to the x-axis and paraell to the y-axis are semi-circular.(adsbygoogle = window.adsbygoogle || []).push({});

that was just the intro, here are the questions:

can someone just help me setup the integral to these three problems?

1.) Local health codes require that the air must completely filtered (or replaced) every half hour for the building. What must be the minimum capacity in cubic feet per minute to of the air handler (pump) to meet the code?

okay this question is kinda confusing. I'm thinking it's a surface area question.here's what i did:

dy/dx = 3x*cos(3x) + sin(3x)

surface area formula:

[tex] S= \int_{a}^{b} 2\pi*x*\sqrt{1+(\frac{dy}{dx})^2}[/tex]

so here's my integral:

[tex] S= \int_{0}^{3\pi} 2\pi*x*\sqrt{1+(3x*cos(3x) + sin(3x))^2}[/tex]

2.) The building will have a fabric exterior similar to a tent. The architect specifies that there must be a reinforcement in the wall for every 10 feet of wall (think arc length) and each end. How many reinforcement must be ordered?

Arc Length Formula = [tex] L = \int_{a}^{b} \sqrt{1+(\frac{dy}{dx})^2}[/tex]

so y' = 3x*cos(3x) + sin(3x) , after that wouldnt i just plug it in the formula?

[tex] L = \int_{0}^{3\pi} \sqrt{1+(3x*cos(3x) + sin(3x))^2}[/tex]

3.) The architect is hoping that people will see the building as waves in the ocean. She has specificed that the exposed exterior surface must be painted in sea-dappled blue paint. If the coverage for a gallon of sea-dapple blue paint. If the coverage for a gallon of sea-dapple blue paint is 100 square feet, how many gallons of paint are required? (then ends will open)

can i use shells to solve this? my integral

[tex] \int_{0}^{100} 2\pi*x*(x*sin(3x)+10)[/tex]

can someone check if my setup for the integrals are correct?

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# Homework Help: Cal 2 help please - hard problem

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