Question

The area of the region bounded by the straight lines \( x = 0 \) and \( x = 2 \) and the curves \( y = 2x^2 \) and \( y = 2x - x^2 \) is equal to

• A. \( 2 \log 2 \)
• B. \( 3 \log 2 \)
• C. \( 4 \log 2 \)
• D. \( 3 \log 2 \)

Hint:

To find the area between two curves, integrate the difference between the functions over the given limits.

Answer 1

The Correct Option is B

Step 1: Set up the integrals.
To find the area between two curves, subtract the lower curve from the upper curve and integrate over the given bounds.

Step 2: Conclusion.
Thus, the correct answer is option (B).

Final Answer: \[ \boxed{\text{(B) } 3 \log 2} \]