Final answer:
The student's question involves sketching the region enclosed by the parabolic equations x = 28 - 7y² and x = 7y² - 28. They should plot the curves to find intersection points and then choose to integrate with respect to y, drawing a typical approximating rectangle with its height given by the x-value difference at a specific y.
Step-by-step explanation:
The student is asked to sketch the region enclosed by the curves x = 28 - 7y² and x = 7y² - 28. To find the region enclosed by these curves, one can plot both equations on the same graph. The first step is to solve for the points of intersection, which involves setting the right-hand sides of the equations equal to determine the y-values where the curves intersect.
After plotting the curves and determining their points of intersection, we need to decide whether to integrate with respect to x or y. The equations suggest that it is more convenient to integrate with respect to y as they are already solved for x.
A typical approximating rectangle for an integral with respect to y would have its height determined by the difference in the x-values of the two curves for a certain y (the width of the rectangle) and its width dy (the height of the rectangle).