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Area of Bounded Regions · Question 23 of 115

What is the area of R?

Question 23

MediumOriginal question

A region $R$ lies in the first quadrant. It is bounded by the $y$ -axis, the lines $y = 1$ and $y = 4$ , and the line $x + y = 6$ .

What is the area of $R$ ?

4.5 square unitsCorrect answerYour answer6 square unitsCorrect answerYour answer10.5 square unitsCorrect answerYour answer15 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\int_1^{4} (6 - y)\,dy = \left[6y - \frac{y^{2}}{2}\right]_1^{4} = (24 - 8) - \left(6 - \frac{1}{2}\right)$ .
$\frac{21}{2}$ square units: a trapezium with parallel sides 5 and 2 and height 3.

Worth noting

15 is the rectangle $5 \times 3$ , as if every strip were as long as the bottom one.

Concept: Area of a region bounded by lines
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsRegions with lines

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