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Finding area between two bounded curves 
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#1
Dec512, 08:59 PM

P: 476

1. The problem statement, all variables and given/known data
f(x) = (x^3) + (x^2)  (x) g(x) = 20*sin(x^2) 2. Relevant equations 3. The attempt at a solution I found the zeroes of the two functions at 4 intersections, and then the zeroes of each function respectively (there's 3 for f(x) and 4 for g(x) between 3 and 3), for certain reference points when I'm making the integration. I did: integral of [g(x) from g(0)_1 to g(0)_2]  integral of [g, x = g(0)_1 intersection_1]  integral of [f from intersection_1 to intersection_2]  integral of [f from intersection_2 to g(0)_2] + integral of [f from intersection_2 f(0)_1]  integral of [g from intersection_2 to g(0)_2] + integral of [g from g(0)_2 to 0]  integral of [f from f(0)_1 to 0] + integral of [f from 0 to f(0)_3] + integral of [g from 0 to intersection_4]  integral of [f from f(0)_3 to intersection_4]  integral of [g from intersection_4 to g(0)_4] I used a graph on the Wolframalpha website as a guide. There's 5 main parts to take the areas of and subtract the respective unnecessary areas. I got 39.19 as my answer but I have no way of checking my solution so I wanted to make sure with more knowledgeable people. 


#2
Dec512, 10:55 PM

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It's not clear to me that the zeroes of the functions have anything to do with it. The title says the area between the curves, not between the curves and some lines parallel to the axes. OTOH, my reading of it implies you need to solve f=g to find the range of integration, and I don't believe there's an analytic solution to that. Further, I've no idea how to integrate sin(x^{2}).
Are you supposed to do this analytically or by approximation? 


#3
Dec512, 11:02 PM

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PF Gold
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[Edit  added later] If the problem is to find the finite area that is bounded by the curves I get 39.45480254 using Maple. 


#4
Dec512, 11:19 PM

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Finding area between two bounded curves



#5
Dec612, 06:29 AM

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PF Gold
P: 39,682

Since there are, in fact, an infinite number of intersections of the two curves, I suspect there was some restriction on x that we were not told.



#6
Dec612, 11:46 AM

P: 476

Which piece(s) and I calculating incorrectly? 


#7
Dec612, 04:06 PM

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P: 9,921




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