What is the area of the region bounded by y = | x |, the x-axis and the lines x = -1 and x = 3?

Question 16

MediumOriginal question

What is the area of the region bounded by $y = \lvert x \rvert$ , the $x$ -axis and the lines $x = -1$ and $x = 3$ ?

4 square unitsCorrect answerYour answer4.5 square unitsCorrect answerYour answer5 square unitsCorrect answerYour answer10 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\lvert x \rvert = -x$ for $x < 0$ and $x$ for $x \ge 0$ , so split at 0: $\int_{-1}^{0} (-x)\,dx + \int_0^{3} x\,dx$ .
$\frac{1}{2} + \frac{9}{2} = 5$ square units.

Worth noting

4 is $\int_{-1}^{3} x\,dx$ , which reads $\lvert x \rvert$ as $x$ : the small triangle left of the $y$ -axis is taken away instead of added.

Concept: Splitting a region where its boundary changes
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsRegions with lines

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What is the area of the region bounded by y=∣x∣y = \lvert x \rverty=∣x∣, the xxx-axis and the lines x=−1x = -1x=−1 and x=3x = 3x=3?

Explanation

What is the area of the region bounded by $y = \lvert x \rvert$ , the $x$ -axis and the lines $x = -1$ and $x = 3$ ?