Question

The area bounded by the curve \(x = 2 - y - y^2\) and the Y-axis is

• A. \(7/6\)
• B. \(13/2\)
• C. \(9/2\)
• D. \(27/2\)

Hint:

When the curve is given as \(x=f(y)\), it is usually best to integrate with respect to \(y\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Area \(= \int_{y_1}^{y_2} x dy\).
Step 2: Key Formula or Approach:
Limits from \(x = 0 \implies y^2+y-2=0 \implies y = -2, 1\).
Step 3: Detailed Explanation:
\[ \int_{-2}^{1} (2-y-y^2) dy = [2y - y^2/2 - y^3/3]_{-2}^{1} = (2-0.5-0.33) - (-4-2+8/3) = 9/2 \] Step 4: Final Answer:
Area is \(9/2\).