Integral

Step 1: Identify the boundaries of the region. The region is bounded by the curve (which is ), the x-axis ( ), and the vertical line . We need to find the point where the curve intersects the x-axis to determine the lower limit of integration. Set : So, the region is bounded by , , , and . Step 2: Set up the definite integral for the area. The area under the curve from to above the x-axis is given by . Here, , , and . Since for , the area is: Step 3: Evaluate the indefinite integral using integration by parts. Let and . Then and . Using the formula : Step 4: Evaluate the definite integral using the limits of integration. Substitute and : Step 5: Compare the result with the given options. The calculated area is 1, which matches option (C).