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anonymous

  • 5 years ago

f(x)=x^3 and g(x)= 2x-x^3, the area enclosed between the origin and the intersection with a positive x is?

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  1. anonymous
    • 5 years ago
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    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.

  2. anonymous
    • 5 years ago
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    tell me what it is and i will help you finish the problem, also make a quick sketch of the area first

  3. anonymous
    • 5 years ago
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    intersection point is x=1

  4. anonymous
    • 5 years ago
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    alright so that will become your upper bound of integration.

  5. anonymous
    • 5 years ago
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    So 1 is your outer boundary, the origin the other: (0,1)

  6. anonymous
    • 5 years ago
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    it asks for the area between the origin and the intersection, so you mean the area between the 2 curves?

  7. anonymous
    • 5 years ago
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    yup

  8. anonymous
    • 5 years ago
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    alright so on your sketch which function lies higher in the y direction?

  9. anonymous
    • 5 years ago
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    g(x)

  10. anonymous
    • 5 years ago
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    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

  11. anonymous
    • 5 years ago
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    soo..\[\int\limits_{0}^{1}g(x)dx-\int\limits_{0}^{1}f(x)dx\]

  12. anonymous
    • 5 years ago
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    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

  13. anonymous
    • 5 years ago
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    so in any case, the function that lies higher will subtract the lower function? to find the area between the curves

  14. anonymous
    • 5 years ago
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    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

  15. anonymous
    • 5 years ago
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    thank you so much! :)

  16. anonymous
    • 5 years ago
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    np

  17. anonymous
    • 5 years ago
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    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.

  18. anonymous
    • 5 years ago
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    alright, i'll keep that in mind, thank you! :)

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