Final answer:
To sketch the region, the curve y=x⁶ is plotted with vertical lines at x=2 and x=7. The area is then computed by integrating the function y=x⁶ from x=2 to x=7.
Step-by-step explanation:
The student has asked to sketch the region bounded by the equations y = 1x⁶, y = 0, x = 2, and x = 7, and then compute the area of this region. To sketch this region, you plot the curve y = 1x⁶ on a graph and then draw vertical lines at x = 2 and x = 7 to represent the boundaries. The horizontal line y = 0 serves as the base of the region on the x-axis. To find the area of the region, you would integrate the function y = 1x⁶ from x = 2 to x = 7.
The correct process to find the area of the shaded region is to calculate the definite integral:
∫27 1x⁶ dx
Note: Since the function provided, y = 1x⁶, is missing a multiplying factor such as 1/x, the sketching and integration process is based on the assumption that the typo is ignored, and y = 1x⁶ represents the polynomial function y = x⁶.