Question

The area of the region bounded by the curve \( x = 2y + 3 \) and lines \( y = 1 \) and \( y = -1 \) is:

• A. 4 sq. units
• B. \( \frac{3}{2} \) sq. units
• C. 6 sq. units
• D. 8 sq. units

Hint:

To find the area between curves and lines, set up an integral with the appropriate limits and integrate the function over the given range.

Answer 1

The Correct Option is C

Step 1: To find the area between the curve and the lines, we need to set up an integral. The equation of the curve is \( x = 2y + 3 \). The bounds for \( y \) are from \( y = -1 \) to \( y = 1 \).
Step 2: The area is given by: \[ \int_{-1}^{1} (2y + 3) \, dy. \] Step 3: Solving the integral, we get an area of 6 sq. units.

Final Answer: \[ \boxed{6 \, \text{sq. units}} \]