What is the area of the parabola $x^2=y$ bounded by the line $y=1$ ?

• A

  $\frac{1}{3}$ square unit
• Correct answer
  B

  $\frac{2}{3}$ square unit
• C

  $\frac{4}{3}$ square units
• D

  2 square units

Solution

Required area is area AOB $\begin{aligned} & =\int_0^1 \sqrt{y} \cdot d y=\left[\frac{(y)^{3 / 2}}{3 / 2}\right]_0^1 \\ & =\frac{2}{3} \text { square units } \end{aligned}$

Hence, the correct answer is option: 'B'.