### INTRO:

Calculating the area of a curved shape can be tricky, especially when it is not a traditional geometric shape. In this article, we will look at how to calculate the area of a region bounded by two curves, y = 6 – x2 and y = x2 – 2x + 2.

### Calculating the Area of a Curve

In order to calculate the area of a curved shape, one must first understand the concept of integration. Integration is a process of calculating the area under a curve by summing up the area of all the small rectangles that make up the curve. This method is most commonly used to calculate the area of a curve that is not a traditional geometric shape.

To calculate the area of the region bounded by two curves, one must first find the bounds of the curves.

### Finding the Bounds of y = 6 – x2 and y = x2 – 2x + 2.

The first step in finding the bounds of the two curves is to solve for the x-intercepts of each curve. The x-intercepts of the first curve, y = 6 – x2, can be found by setting y = 0 and solving for x. This gives us the x-intercepts of x = ±2√3. The x-intercepts of the second curve, y = x2 – 2x + 2, can be found by setting y = 0 and solving for x. This gives us the x-intercepts of x = 1 ± √3.

Once the x-intercepts have been found, the next step is to find the y-intercepts of each curve. The y-intercepts of the first curve, y = 6 – x2, can be found by setting x = 0 and solving for y. This gives us the y-intercepts of y = 6. The y-intercepts of the second curve, y = x2 – 2x + 2, can be found by setting x = 0 and solving for y. This gives us the y-intercepts of y = 2.

With the x-intercepts and y-intercepts of the two curves, we can now calculate the area of the region bounded by the two curves.

### OUTRO:

In conclusion, calculating the area of a curved shape can be done by finding the bounds of the curves and using integration to calculate the area of all the small rectangles that make up the curve. In this article