Read the two statements and choose the correct option. I. The region bounded by y = 2x, the x-axis and the line x = 3 has the same area as the region bounded by x = y/2, the y-axis and the line y = 6. II. ∫₋₁^1 x dx is the area of the region bounded by y = x, the x-axis and the lines x = -1 and x = 1.

Question 19

MediumOriginal question

Read the two statements and choose the correct option.
I. The region bounded by $y = 2x$ , the $x$ -axis and the line $x = 3$ has the same area as the region bounded by $x = \frac{y}{2}$ , the $y$ -axis and the line $y = 6$ .
II. $\int_{-1}^{1} x\,dx$ is the area of the region bounded by $y = x$ , the $x$ -axis and the lines $x = -1$ and $x = 1$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $\int_0^{3} 2x\,dx = 9$ and $\int_0^{6} \frac{y}{2}\,dy = 9$ ; the two triangles together fill the rectangle $3 \times 6$ . True.
II: $\int_{-1}^{1} x\,dx = 0$ , but the region is two triangles of area $\frac{1}{2}$ each, 1 in all. False.

Worth noting

Taking II as true lets the triangle below the axis cancel the one above; an area adds their sizes.

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