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 = 5/x, y = 10/x2, x = 6.

Answer 1

To sketch the region enclosed by the given curves, we need to find the intersection points and determine whether to integrate with respect to x or y. The intersection point is (2,5) and we should integrate with respect to x. We can draw a typical approximating rectangle to evaluate the area under the curve.

Step-by-step explanation:

To sketch the region enclosed by the given curves, we need to find the intersection points of the curves and determine whether to integrate with respect to x or y.

Let's find the intersection points:

At the intersection of y = 5/x and y = 10/x², we have:

5/x = 10/x²
5x = 10
x = 2

So the intersection point is (2,5).

Next, we need to determine whether to integrate with respect to x or y. Looking at the given curves, it is clear that the curve y = 5/x is above the curve y = 10/x². Therefore, we should integrate with respect to x.

To draw the typical approximating rectangle, we can choose a small interval of x-values (e.g., (2,6)) and divide it into n subintervals. We can then evaluate the area under the curve by summing the areas of the rectangles.