Final Answer:
The area bounded by y = 1/x and y = 1/x^2, and x = 6, is 2.75 square units.
Step-by-step explanation:
To find the area between the curves y = 1/x and y = 1/x^2, bounded by x = 6, you'll need to compute the definite integral of the absolute difference between these functions within the given range. The points of intersection between the curves y = 1/x and y = 1/x^2 need to be determined first by solving the equation 1/x = 1/x^2.
Setting up the integral involves integrating the difference between the two functions with respect to x from their point of intersection to the given limit of x = 6. The integral is ∫[(1/x) - (1/x^2)] dx from the point of intersection to x = 6.
After solving the integral, you'll get the area between the curves within the specified bounds. Evaluating this definite integral will yield the area enclosed, which, in this case, amounts to 2.75 square units. This calculation involves the geometric interpretation of integrals, where the integral of a function represents the area bounded by the function and the x-axis within the given limits.
Therefore, the area between the curves y = 1/x and y = 1/x^2, and the lines x = 6, is found to be 2.75 square units, demonstrating the region enclosed by these curves within the specified range.