## anonymous one year ago Find the area of the region bounded by the functions f(x) = x4 and g(x) = |x|.

1. anonymous

@jim_thompson5910

2. 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

3. jim_thompson5910

in Q1, x > 0 when x > 0, |x| = x So when x > 0, g(x) = x

4. jim_thompson5910

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

5. anonymous

x=1 and x=0

6. IrishBoy123

$\checkmark$

7. 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

8. Loser66

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

9. jim_thompson5910

yes because of symmetry about the y axis

10. Loser66

|dw:1444438095472:dw|

11. Loser66

|dw:1444438146262:dw|

12. jim_thompson5910

13. jim_thompson5910

$\Large \int_{0}^{1}\left(x-x^4\right)dx$ takes care of the right half. Double it to get both halves

14. Loser66

oh, so the function is not x^4 =x, it should be x^4 =|x| to get both.

15. jim_thompson5910

I made it g(x) = x when just focusing on when x > 0 (in quadrant 1)

16. jim_thompson5910

to simplify the absolute value

17. Loser66

Got you. Thanks for explanation :)

18. jim_thompson5910

no problem

19. anonymous

I got 0.6 as the final answer.