Question

For which of the following values of \( m \), the area of the region bounded by the curve \( y = x - x^2 \) and the line \( y = mx \) equals 5?

• A. \( -4 \)
• B. \( -2 \)
• C. \( 2 \)
• D. \( 4 \)

Hint:

To find the area between curves, integrate the difference of the functions over the range of intersection.

Answer 1

The Correct Option is B

Step 1: Understanding the problem.
We are given the curves \( y = x - x^2 \) and \( y = mx \), and we need to find the value of \( m \) such that the area enclosed by the curves is 5. This can be done by setting up the area integral and solving for \( m \).

Step 2: Conclusion.
The value of \( m \) is \( -2 \), corresponding to option (2).