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anonymous

  • one year ago

Find the area of the region bounded by the functions f(x) = x4 and g(x) = |x|.

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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    since both are even functions, you can focus on the portion in Q1 then just double that result to get the full area

  3. jim_thompson5910
    • one year ago
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    in Q1, x > 0 when x > 0, |x| = x So when x > 0, g(x) = x

  4. jim_thompson5910
    • one year ago
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    solve x^4 = x to find out where the two functions cross

  5. anonymous
    • one year ago
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    x=1 and x=0

  6. IrishBoy123
    • one year ago
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    \[\checkmark\]

  7. jim_thompson5910
    • one year ago
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    so you need to compute \[\Large 2*\int_{0}^{1}\left(g(x) - f(x)\right)dx\] where f(x) = x^4 g(x) = x

  8. Loser66
    • one year ago
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    I don't think we get 2 in the front @jim_thompson5910

  9. jim_thompson5910
    • one year ago
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    yes because of symmetry about the y axis

  10. Loser66
    • one year ago
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    |dw:1444438095472:dw|

  11. Loser66
    • one year ago
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    |dw:1444438146262:dw|

  12. jim_thompson5910
    • one year ago
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  13. jim_thompson5910
    • one year ago
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    \[\Large \int_{0}^{1}\left(x-x^4\right)dx\] takes care of the right half. Double it to get both halves

  14. Loser66
    • one year ago
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    oh, so the function is not x^4 =x, it should be x^4 =|x| to get both.

  15. jim_thompson5910
    • one year ago
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    I made it g(x) = x when just focusing on when x > 0 (in quadrant 1)

  16. jim_thompson5910
    • one year ago
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    to simplify the absolute value

  17. Loser66
    • one year ago
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    Got you. Thanks for explanation :)

  18. jim_thompson5910
    • one year ago
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    no problem

  19. anonymous
    • one year ago
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    I got 0.6 as the final answer.

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