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anonymous

  • 4 years ago

the functions f and g are given f=sqrt(x) and g = 6-x. Let R be the region bounded by the x-axis and the graphs of f and g. Find the area of R

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  1. anonymous
    • 4 years ago
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    can someone help

  2. TuringTest
    • 4 years ago
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    first step is to get an idea of the shape of the area:|dw:1329269119785:dw|it looks like we will have to do two separate integrals, because we can see that before the line x=xo we have the area as g-f, and after given by f-g. xo occurs when the functions intersect, so we can find it by solving\[f(x)=g(x)\]for x. our integral to find R will then be\[R=\int_{0}^{x_o}g-fdx+\int_{x_o}^{6}f-gdx\]

  3. anonymous
    • 4 years ago
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    i found the intersection point between the two curve and its (4,2) so i integrated from 0 to 4 and did f - g why is that wrong?

  4. TuringTest
    • 4 years ago
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    whoa sorry, misread just\[R=\int_{0}^{x_o}fdx+\int_{x_o}^{6}gdx\]

  5. anonymous
    • 4 years ago
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    i get what you are saying their but i am a little confuse to how to know what integral to set up

  6. anonymous
    • 4 years ago
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    btw thanks for the help

  7. TuringTest
    • 4 years ago
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    you found that the intersection point is at x=4|dw:1329269909705:dw|the first area is under f so it is\[R_1=\int_{0}^{4}fdx\]the second area is under g so it is\[R_2=\int_{4}^{6}gdx\]the total area is then\[R=R_1+R_2=\int_{0}^{4}fdx+\int_{4}^{6}gdx\]

  8. TuringTest
    • 4 years ago
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    |dw:1329270195071:dw|

  9. anonymous
    • 4 years ago
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    I guess its wrong to why is it wrong to integrate for 0 to 6 of f - g...your pic is very good i get that...but i dont get why you can just integrate from 0 to 6

  10. TuringTest
    • 4 years ago
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    g>f for 0<x<4, so f-g would be negative. we want a positive area Imagine there were no g. You can see that R1 would be given by the integral of f from 0 to 4 either way, so excluding g on that interval will give us the right answer f-g for 4<x<6 would be the black area on the following graph area:|dw:1329270527650:dw| so you can see that is not right either.

  11. TuringTest
    • 4 years ago
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    \[\int_{0}^{4}fdx\]is this area:|dw:1329270801204:dw|

  12. TuringTest
    • 4 years ago
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    \[\int_{4}^{6}gdx\]would be this|dw:1329270875759:dw|

  13. TuringTest
    • 4 years ago
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    \[\int_{0}^{4}g-fdx\]would be this|dw:1329270925750:dw|it is important to think of the shape of each area...

  14. anonymous
    • 4 years ago
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    Ok great explanations that you!!!

  15. TuringTest
    • 4 years ago
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    welcome :D

  16. anonymous
    • 4 years ago
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    I will definately be asking more questions ....hope you can help me...lol i am sure you can

  17. TuringTest
    • 4 years ago
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    hope so :)

  18. anonymous
    • 4 years ago
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    let me find some more

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