Parabolas And Area Under Curves

Step 1: Recall the equation of the parabola.
The given equation is , which is the standard form of a parabola opening to the right with vertex at the origin.

Step 2: Find the focus and latus rectum.
For the parabola , we have , so . The focus is at , and the length of the latus rectum is .

Step 3: Set up the integral for the area.
The area of the region bounded by the parabola and its latus rectum can be found by integrating the curve from to (the x-coordinate of the focus):

Step 4: Solve the integral.
Now, solve the integral:

Step 5: Conclude the solution.
Thus, the area of the region is square units.

Final Answer: