question_answer

What is the area of the parabola \[{{x}^{2}}=y\] bounded by the line y = 1?

A) \[\frac{1}{3}\] square unit

B) \[\frac{2}{3}\] square unit

C) \[\frac{4}{3}\] square units

D) 2 square units

Correct Answer: C

Solution :

[c] Area of \[ABCD=2\times 1=2\] sq. units Area of \[BAODC=\int_{-1}^{1}{{{x}^{2}}}dx=\left. \frac{{{x}^{3}}}{3} \right|_{-1}^{1}=\frac{2}{3}\] sq. units Required area \[=2-\frac{2}{3}=\frac{4}{3}\] sq. units