# How to find the area of the region bounded by the curves y = x^4 and y = 8x ?

##### 1 Answer

Mar 13, 2018

The area is

#### Explanation:

We start by finding their points of intersection .

#x^4 = 8x#

#x^4 - 8x = 0#

#x(x^3 - 8) 0#

#x = 0 or x^3 = 8#

#x= 0 or x = 2#

These will be our bounds of integration.

We also see that on

Our expression for area will therefore be

#A = int_0^2 8x - x^4dx#

#A = [4x^2 - 1/5x^5]_0^2#

#A = 4(2)^2 - 1/5(2)^5#

#A = 16 - 32/5#

#A = 48/5#

Thus, the area between the two curves is

Hopefully this helps!