The area (in sq. units) bounded by a parabola y^2=4x and its latus rectum, is Option 1: 8/3 Option 2: 4/3 Option 3: 2/3 Option 4: 16/3

Answer: 8/3. Solution: For y^2=4x, a=1, so the latus rectum is the line x=1. Area = 2_0^1 2√x dx = 4*2/3 = 8/3 square units.

Calculus

Application of Integrals

Easy

applied

The area (in sq. units) bounded by a parabola $y^2=4x$ and its latus rectum, is

$\frac{8}{3}$

$\frac{4}{3}$

$\frac{2}{3}$

$\frac{16}{3}$

✅ Correct Option: 1

For $y^2=4x$ , $a=1$ , so the latus rectum is the line $x=1$ .

Area $= 2\int_0^1 2\sqrt{x}\,dx = 4\cdot\frac{2}{3} = \frac{8}{3}$ square units.

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