Question

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

Answer 1

@jim_thompson5910

Answer 2

since both are even functions, you can focus on the portion in Q1 then just double that result to get the full area

Answer 3

in Q1, x > 0

when x > 0, |x| = x

So when x > 0, g(x) = x

Answer 4

solve x^4 = x to find out where the two functions cross

Answer 5

x=1 and x=0

Answer 6

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Answer 7

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

Answer 8

I don't think we get 2 in the front @jim_thompson5910

Answer 9

yes because of symmetry about the y axis