Applications Of Integrals

We are given the curve and the line . To find the area bounded by the curve and the line, we first need to find the points of intersection of these two functions.
Step 1: Find the points of intersection Set to find the points of intersection: Thus, and are the points of intersection.
Step 2: Set up the integral for the area The area between the curve and the line from to is given by the integral: Simplify the integrand: Thus, the area is:
Step 3: Compute the integral Integrate : Now evaluate the definite integral:

The correct option is (A) :