SOLUTION: find the integral for the surface area of the surface of revolution and approximate the integral with a numerical method : y=4cosx, 0<= x <= pi/4, revolved about the x axis ?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: find the integral for the surface area of the surface of revolution and approximate the integral with a numerical method : y=4cosx, 0<= x <= pi/4, revolved about the x axis ?       Log On


   

Question 873205: find the integral for the surface area of the surface of revolution and approximate the integral with a numerical method :
y=4cosx, 0<= x <= pi/4, revolved about the x axis ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-1%2C2%2C-5%2C5%2C4cos%28x%29%29
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y=4cos%28x%29
dy%2Fdx=-4sin%28x%29
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A=int%282%2Api%2Ay%2Cds%2Cx=0%2Cpi%2F4%29
ds=sqrt%281%2B%28dy%2Fdx%29%5E2%29dx
ds=sqrt%281%2B16sin%5E2%28x%29%29dx
A=2%2Api%2Aint%284cos%28x%29%2Asqrt%281%2B16sin%5E2%28x%29%29%2Cdx%2Cx=0%2Cpi%2F4%29
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I used a modified Simpson's rule and got,
A=5.405