Let A₁ be the area bounded by the parabola y^2 = 4x and the line x = 1, and A₂ the area bounded by the same parabola and the line x = 4. What is (A₂)/(A₁)?

Area of Bounded Regions · Question 78 of 115

Question 78

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Let $A_1$ be the area bounded by the parabola $y^{2} = 4x$ and the line $x = 1$ , and $A_2$ the area bounded by the same parabola and the line $x = 4$ . What is $\frac{A_2}{A_1}$ ?

2

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4

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8

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16

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CorrectNot quiteAnswer C

Correct answer: C

Up to $x = c$ the area is $2\int_0^{c} 2\sqrt{x}\,dx = \frac{8}{3}c^{3/2}$ : $A_1 = \frac{8}{3}$ and $A_2 = \frac{8}{3} \times 8 = \frac{64}{3}$ .
$\frac{A_2}{A_1} = 4^{3/2} = 8$ .

Worth noting

4 assumes the area grows like $c$ ; it grows like $c^{3/2}$ , because the region also gets taller as it gets longer.

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

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