The figure shows the region bounded by the parabola y^2 = 8x and the line x = 2, its latus rectum. What is its area? The parabola y² = 8x opening to the right, with the region up to the line x = 2 shaded

The figure shows the region bounded by the…

The figure shows the region bounded by the parabola y^2 = 8x and the line x = 2, its latus rectum.

MediumOriginal question

The figure shows the region bounded by the parabola $y^{2} = 8x$ and the line $x = 2$ , its latus rectum. What is its area?

\frac{16}{3}

square unitsCorrect answerYour answer8 square unitsCorrect answerYour answer

\frac{32}{3}

square unitsCorrect answerYour answer16 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The region is symmetric about the $x$ -axis: $2\int_0^{2} \sqrt{8x}\,dx$ .
$2\sqrt{8} \cdot \frac{2}{3}x^{3/2}\Big|_0^{2} = 2 \times \frac{16}{3} = \frac{32}{3}$ square units.

Worth noting

$\frac{16}{3}$ is the half above the $x$ -axis.

Ten questions from Area of Bounded Regions, at your own pace.

Ten questions from Area of Bounded Regions, at your own pace.