Final answer:
To calculate the area under the sine squared function (y = sin² x), we need to integrate it over a specific interval. This involves using the double-angle identity for cosine. The bounds of integration must be specified for an exact answer.
Step-by-step explanation:
To find the area of a region defined by the function y = sin² x, we should consider integrating the function with respect to x over a certain interval. The definite integral of a function represents the accumulated area under the curve from one point to another on the x-axis.
The integral of sin² x can be more complicated than basic functions because it involves a trigonometric identity. The double-angle identity for cosine can be useful in simplifying the integral of sin² x:
sin² x = ½(1 - cos(2x)).
Integrating this over an interval from x1 to x2, you would get the area under the curve within that interval. The exact bounds of integration were not specified in the question, so this general approach is outlined.
Note that when we carry out such calculations, it is important to use sufficient significant figures to ensure accuracy during intermediate steps, just as you would in finding the inverse sine or converting between degrees and radians.