Area Under Simple Curves

The given equation is a parabola. To find the area, we first express as: The area is given by the integral of from to : Now, compute the integral: Substitute the limits: Now calculate the values: Thus, the area is: The area of the region is:

To find the area between the curve and the line , we first find the points of intersection. Set , which gives: Thus, the points of intersection are and . The area is given by the integral: Now, compute the integral: Substitute the limits: Simplifying: Thus, the area is: The area of the region is: