Question

Find the area bounded by the curves \( y = 2x \) and \( y = x^2 \):

• A. \( \frac{2}{3} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{4}{3} \)
• D. \( 3 \)
• E. \( 2 \)

Hint:

When calculating the area between curves, always subtract the lower function from the upper one.

Answer 1

The Correct Option is C

The area between the curves is given by: \[ A = \int_{0}^{2} (2x - x^2) \, dx \] Evaluating the integral: \[ A = \left[ x^2 - \frac{x^3}{3} \right]_{0}^{2} = \frac{4}{3} \]