Question

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 unit
• D. $2$ square unit

Answer 1

The correct option is C $\frac{4}{3}$ square unit

Here, the area is symmetric about y-axis, we can find the area on one side and then multiply it by $2$, we will get the area,

So required area $=2{\int }_0^1(1-x^2).dx$

$=2{[x-\frac{x^3}{3}]}_0^1$

$=\frac{4}{3}$

Hence, C is correct.