What is the area of the region between the lines $y = 2x$ and $y = x$ from $x = 0$ to $x = 3$ ?

3 square unitsCorrect answerYour answer4.5 square unitsCorrect answerYour answer9 square unitsCorrect answerYour answer13.5 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

On $0 \le x \le 3$ , $y = 2x$ is the upper line: $\int_0^{3} (2x - x)\,dx$ .
$\frac{9}{2}$ square units.

Worth noting

9 is the area under $y = 2x$ alone, without taking away the region under $y = x$ .

Concept: Area between two lines
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsRegions with lines

Practise this chapter →

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

Practise this chapter →

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

Practise this chapter All 115 questions in Area of Bounded Regions Revise the notes for Area of Bounded Regions

What is the area of the region between the lines y=2xy = 2xy=2x and y=xy = xy=x from x=0x = 0x=0 to x=3x = 3x=3?

Explanation

What is the area of the region between the lines $y = 2x$ and $y = x$ from $x = 0$ to $x = 3$ ?