anonymous
  • anonymous
Find the area of the region bounded by the functions f(x) = x4 and g(x) = |x|.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
since both are even functions, you can focus on the portion in Q1 then just double that result to get the full area
jim_thompson5910
  • jim_thompson5910
in Q1, x > 0 when x > 0, |x| = x So when x > 0, g(x) = x

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More answers

jim_thompson5910
  • jim_thompson5910
solve x^4 = x to find out where the two functions cross
anonymous
  • anonymous
x=1 and x=0
IrishBoy123
  • IrishBoy123
\[\checkmark\]
jim_thompson5910
  • jim_thompson5910
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
Loser66
  • Loser66
I don't think we get 2 in the front @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
yes because of symmetry about the y axis
Loser66
  • Loser66
|dw:1444438095472:dw|
Loser66
  • Loser66
|dw:1444438146262:dw|
jim_thompson5910
  • jim_thompson5910
jim_thompson5910
  • jim_thompson5910
\[\Large \int_{0}^{1}\left(x-x^4\right)dx\] takes care of the right half. Double it to get both halves
Loser66
  • Loser66
oh, so the function is not x^4 =x, it should be x^4 =|x| to get both.
jim_thompson5910
  • jim_thompson5910
I made it g(x) = x when just focusing on when x > 0 (in quadrant 1)
jim_thompson5910
  • jim_thompson5910
to simplify the absolute value
Loser66
  • Loser66
Got you. Thanks for explanation :)
jim_thompson5910
  • jim_thompson5910
no problem
anonymous
  • anonymous
I got 0.6 as the final answer.

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