region bounded

Question

Find the area of the region bounded by the functions f(x) = x4 and g(x)= square root lxl


7/15

14/15

28/15
None of these

Answer 1

The answer should be 14/15 

 

Focus on one side of the graph first sometimes visually representing it can help

 

you basically have sqrt(x) reflected accross the y axis (sqrt(|x|)) and a real steep parabola (x^4).

 

The graphs will intersect at 0, 1, and -1. Looking at the right side the parabola will be under

the sqrt graph. (sqrt(0.5) > 0.5^4)

 

Calculating the area under the sqrt(|x|) you can just use sqrt(x) to find the area under the right side

 

This is the same as x^0.5

 

Integral from 0-1 of x^0.5 is 2/3

 

Next step is to subtract the area under the parabola which can be found by taking the integral

of x^4 on 0-1.

 

This comes out to 1/5.  

 

2/3 - 1/5 = 7/15 

 

Since there are 2 sides to the graph you multiply by 2 giving 14/15