Area of the region inside the unit circle

In summary, the question is asking for the area inside the unit circle and above the graph of the function f(x) = x^5. The suggested approach is to find the points of intersection between the unit circle and the graph of the function, but this requires solving a 10th degree equation with no easy solutions.
  • #1
aznboi855
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Homework Statement



The area in the region inside the unit circle and above the graph of f(x) = x^5

Homework Equations



I don't know how to type the equation in here but the area is the integral between two integration points of the higher curve minus the lower curve.

The Attempt at a Solution



I tried using the integration points 0 and 2.02381 (the farthest the graph will stretch out according to derive), but that's the area outside and under the curve, i think the question is asking for the area INSIDE the curve.
As far as I know you can't do it with respect to y because it's infinite.

Thanks.
 
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  • #2
I'm not sure why you'd be using those integration points. For a unit circle, what is the largest possible value of x and/or y? Or, maybe think about the equation for a unit circle. Where does f(x) cross the unit circle?
 
  • #3
(1,1)? So it'll be from 0 to 1 correct?

If we were to do it that way, the point of intersection would be 1 and I'm guessing the radius will be on top of the curve?
So it'll be... SQRT(1-x^2) - (x^5)?
 
  • #4
(1, 1) is not a point on the circle.

Finding the points of intersection entails solving the equation sqrt(1 - x^2) = x^5. If you square both sides, you get a 10th degree equation that has no easy-to-get solutions.
 

Related to Area of the region inside the unit circle

What is the unit circle?

The unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on a coordinate plane. It is used in mathematics to understand the properties of trigonometric functions.

What is the formula for finding the area of a region inside the unit circle?

The formula for finding the area of a region inside the unit circle is A = πr², where r is the radius of the circle. Since the radius of the unit circle is 1, the formula simplifies to A = π.

Why is the unit circle important?

The unit circle is important because it serves as a reference for understanding the properties of trigonometric functions. It also helps in visualizing and solving problems involving angles and circular motion.

How do you find the area of a specific region inside the unit circle?

To find the area of a specific region inside the unit circle, you will need to determine the boundaries of the region and then calculate the area using the formula A = πr². If the region is a sector, you will also need to use the central angle to find the area.

Can the area of a region inside the unit circle be negative?

No, the area of a region inside the unit circle cannot be negative. The unit circle is a perfect circle, and the area of any region inside a circle is always a positive value.

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