Final answer:
The area of the region enclosed between the curves y = tan²x and y = sin²x from x = -π/4 to x = π/4 can be found by setting up two integrals and subtracting the area under sin²x from the area under tan²x within those bounds.
Step-by-step explanation:
To find the area of the region enclosed between the curves y = tan2x and y = sin2x from x = -π/4 to x = π/4, we set up an integral. Since we are given a range over which to integrate, the area can be found by subtracting the area under the second function from the area under the first function within these bounds.
- Calculate the integral of y = tan2x from x = -π/4 to x = π/4.
- Calculate the integral of y = sin2x from x = -π/4 to x = π/4.
- Subtract the second integral from the first to get the enclosed area.
However, to provide an accurate answer, we would need to have the correct second function, as the notation y = ² x is not clear. Assuming it is a typo and you meant y = sin2x, the enclosed area would then be the difference of the two integrals over the given interval.