Final answer:
To plot the graphs corresponding to the integrals, we need to evaluate the integrals I and J. The integral I is calculated as the area under the curve of sin^2(x) between x=0 and x=2. The integral J is calculated in a similar manner, but using the function cos^2(x) instead.
Step-by-step explanation:
To plot the graphs corresponding to the integrals, we first need to evaluate the integrals I = ∫02 πsin²(x)dx and J = ∫02 πcos²(x)dx. Let's start with I:
We know that ∫02 sin²(x)dx is equal to the area under the curve of sin²(x) between x=0 and x=2. To evaluate this integral, we can use the geometric interpretation of the integral as the area under the curve.
If we plot the function y = sin²(x), we can observe that the curve is a half-period of a sine wave, bounded between the x-axis and the curve. Therefore, the area under the curve can be divided into smaller rectangles with widths dx and heights sin²(x).
A similar approach can be used to evaluate J, which is the integral ∫02 πcos²(x)dx. However, this time the function is y = cos²(x), and the area under the curve represents the integral J.