
#1
Dec512, 08:59 PM

P: 459

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

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,160

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

HW Helper
Thanks
PF Gold
P: 7,197

[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

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,160

Finding area between two bounded curves 



#5
Dec612, 06:29 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882

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: 459

Which piece(s) and I calculating incorrectly? 



#7
Dec612, 04:06 PM

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,160




Register to reply 
Related Discussions  
Area bounded by two curves  Calculus & Beyond Homework  9  
Area bounded by these lines and curves  Calculus & Beyond Homework  2  
Area bounded by polar curves  Introductory Physics Homework  5  
area bounded by the two curves  Introductory Physics Homework  1  
Area bounded by curves  Calculus  9 