CBSE Class 12 · 2024 · Area Under CurvesMultiple Choice

Area of the region bounded by curve

y^{2} = 4 x

and

x = 1

is :

Answer: (B)

Solution

The parabola

y^{2} = 4 x

is symmetric about the

x

-axis, and the line

x = 1

closes off the region on the right.
For

0 \leq x \leq 1

the curve gives

y = \pm 2 x

, so a vertical strip running from the lower branch to the upper branch has height

2 \cdot 2 x = 4 x

A = \int_{0}^{1} 4 x d x = 4 \cdot \frac{2}{3} x^{3/2}_{0}^{1} = \frac{8}{3} .

Hence the required area is

\frac{8}{3}

square units, so the correct option is (B).

CBSE Class 12 Board · 2024 · Single correct option