anonymous
  • anonymous
f(x)=x^3 and g(x)= 2x-x^3, the area enclosed between the origin and the intersection with a positive x is?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
do 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
  • anonymous
tell me what it is and i will help you finish the problem, also make a quick sketch of the area first
anonymous
  • anonymous
intersection point is x=1

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anonymous
  • anonymous
alright so that will become your upper bound of integration.
anonymous
  • anonymous
So 1 is your outer boundary, the origin the other: (0,1)
anonymous
  • anonymous
it asks for the area between the origin and the intersection, so you mean the area between the 2 curves?
anonymous
  • anonymous
yup
anonymous
  • anonymous
alright so on your sketch which function lies higher in the y direction?
anonymous
  • anonymous
g(x)
anonymous
  • anonymous
correct 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
  • anonymous
soo..\[\int\limits_{0}^{1}g(x)dx-\int\limits_{0}^{1}f(x)dx\]
anonymous
  • anonymous
you 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
  • anonymous
so in any case, the function that lies higher will subtract the lower function? to find the area between the curves
anonymous
  • anonymous
yep, 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
  • anonymous
thank you so much! :)
anonymous
  • anonymous
np
anonymous
  • anonymous
Be 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
  • anonymous
alright, i'll keep that in mind, thank you! :)

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