For $m > 0$ , the region bounded by $y = mx$ , the $x$ -axis and the line $x = 3$ has the same area as the triangle bounded by $x + y = 6$ and the coordinate axes. What is $m$ ?

2

Correct answerYour answer

4

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6

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8

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\int_0^{3} mx\,dx = \frac{9m}{2}$ , and the triangle has area $\int_0^{6} (6 - x)\,dx = 18$ .
$\frac{9m}{2} = 18$ gives $m = 4$ .

Worth noting

2 takes $\int_0^{3} mx\,dx$ as $9m$ , dropping the $\frac{1}{2}$ from $\frac{x^{2}}{2}$ .

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

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

For m>0m > 0m>0, the region bounded by y=mxy = mxy=mx, the xxx-axis and the line x=3x = 3x=3 has the same area as the triangle bounded by x+y=6x + y = 6x+y=6 and the coordinate axes. What is mmm?