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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.
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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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3since both are even functions, you can focus on the portion in Q1 then just double that result to get the full area

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3in Q1, x > 0 when x > 0, x = x So when x > 0, g(x) = x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3solve x^4 = x to find out where the two functions cross

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3so 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
 one year ago
Best ResponseYou've already chosen the best response.0I don't think we get 2 in the front @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3yes because of symmetry about the y axis

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3\[\Large \int_{0}^{1}\left(xx^4\right)dx\] takes care of the right half. Double it to get both halves

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0oh, so the function is not x^4 =x, it should be x^4 =x to get both.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3I made it g(x) = x when just focusing on when x > 0 (in quadrant 1)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3to simplify the absolute value

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Got you. Thanks for explanation :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 0.6 as the final answer.
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