Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Enclosed by y = x and y = x^4

Didn't we go through this with you yesterday ???

http://www.jiskha.com/display.cgi?id=1387091654

the answer wasn't correct and I tried to do it myself and it is not working

To find the area of the region enclosed by the curves y = x and y = x^4, we need to determine the points where the two curves intersect. Once we have identified these points, we can set up the integral to calculate the area.

First, let's graph the curves y = x and y = x^4 to visualize the region:

- The graph of y = x is a straight line that passes through the origin (0,0) and has a slope of 1.
- The graph of y = x^4 is a symmetric curve that is centered at the origin but reaches higher values for positive x-values.

By sketching the graphs, we can see that the curves intersect at two points: (0, 0) and (1, 1).

To find the area between two curves, we integrate the difference between the upper curve and the lower curve with respect to x. In this case, the upper curve is y = x, and the lower curve is y = x^4.

The integral to find the area is given by

A = ∫[a, b] (f(x) - g(x)) dx

where f(x) is the upper curve and g(x) is the lower curve, and a and b are the x-values of the intersection points.

In this case, the bounds of integration are from 0 to 1, and the integral becomes:

A = ∫[0, 1] (x - x^4) dx

Using technology or integrating by hand, we find:

A = [x^2/2 - x^5/5] |[0, 1]

A = (1/2 - 1/5) - (0/2 - 0/5)

A = 1/2 - 1/5

Simplifying, we get:

A = 3/10

Therefore, the area of the region enclosed by the curves y = x and y = x^4 is 3/10 square units.

the curves intersect at x=0,1

Now go for it.