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

The area is

We start by finding their points of intersection .

These will be our bounds of integration.

Our expression for area will therefore be

Hopefully this helps!

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To find the area of the region bounded by the curves (y = x^4) and (y = 8x), you need to first determine the points of intersection of the two curves. Then, integrate the absolute difference between the two functions over the interval of intersection from the x-coordinate of the leftmost intersection point to the x-coordinate of the rightmost intersection point. This integral represents the area between the curves.

- Find the points of intersection by setting the two functions equal to each other and solving for x.
- Integrate the absolute difference between the functions over the interval determined by the intersection points.

The integral setup is:

[Area = \int_{x_1}^{x_2} |(8x) - (x^4)| , dx]

Where (x_1) and (x_2) are the x-coordinates of the intersection points.

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