Question

sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. y = 3/x, y = 6/x², x = 5

Answer 1

To sketch the region enclosed by the given curves y = 3/x and y = 6/x², and x = 5, we can find the intersection points and integrate with respect to y.

Step-by-step explanation:

To sketch the region enclosed by the given curves, we need to find the intersection points of the curves and the boundary lines. The given curves are y = 3/x and y = 6/x^2. The boundary line is x = 5.

To find the intersection points, we equate the two curves: 3/x = 6/x^2. Cross multiplying gives us 3x^2 = 6x. Solving for x, we get x = 2.

Now we can sketch the region enclosed by the curves and the boundaries. Since the curves are expressed in terms of y, we will integrate with respect to y. We integrate the upper curve (y = 3/x) from y = 0 to y = 6/5, and then integrate the lower curve (y = 6/x^2) from y = 6/5 to y = ∞.