Using integration, what is the area of the triangle bounded by $y = x$ , $y = 8 - x$ and the $x$ -axis?

8 square unitsCorrect answerYour answer16 square unitsCorrect answerYour answer32 square unitsCorrect answerYour answer64 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The lines meet at $(4, 4)$ and cut the $x$ -axis at 0 and 8.
$\int_0^{4} x\,dx + \int_4^{8} (8 - x)\,dx = 8 + 8 = 16$ square units.

Worth noting

32 uses base $\times$ height without the $\frac{1}{2}$ .

Concept: Area of a region bounded by lines
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsRegions with lines

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Using integration, what is the area of the triangle bounded by y=xy = xy=x, y=8−xy = 8 - xy=8−x and the xxx-axis?

Explanation

Using integration, what is the area of the triangle bounded by $y = x$ , $y = 8 - x$ and the $x$ -axis?