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anonymous
 5 years ago
f(x)=x^3 and g(x)= 2xx^3, the area enclosed between the origin and the intersection with a positive x is?
anonymous
 5 years ago
f(x)=x^3 and g(x)= 2xx^3, the area enclosed between the origin and the intersection with a positive x is?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know how to do a double integral or just single integrals there are several ways to tackle this, in either case find the intersection point first of all.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0tell me what it is and i will help you finish the problem, also make a quick sketch of the area first

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0intersection point is x=1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright so that will become your upper bound of integration.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So 1 is your outer boundary, the origin the other: (0,1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it asks for the area between the origin and the intersection, so you mean the area between the 2 curves?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright so on your sketch which function lies higher in the y direction?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0correct so the area between 0,0 and g(x)  the area between 0,0 and f(x) will be the area that is squeezed in between

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0soo..\[\int\limits_{0}^{1}g(x)dx\int\limits_{0}^{1}f(x)dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can also do a double integral but im not sure what level of calculus you are studying so this should do in any case

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so in any case, the function that lies higher will subtract the lower function? to find the area between the curves

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yep, because if you think of it visually g(x) lies higher in the y direction so the area under g(x) is bigger than f(x), Then subtracting the area under f(x) from g(x) will give you the are between g and f

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much! :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Be careful slim, to your question, that is the case in this problem because you are integrating along the x axis. Be alert that in the future you tackle some problem along the y axis and it would be certainly different. But don't worry about that until you get to it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, i'll keep that in mind, thank you! :)
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