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Area of Bounded Regions · Question 22 of 115

Which integral gives the area of R?

Question 22

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 $x + y = 6$ .

Which integral gives the area of $R$ ?

\int_0^{4} (6 - y)\,dy

Correct answerYour answer

\int_2^{5} (6 - y)\,dy

Correct answerYour answer

\int_1^{4} (y - 6)\,dy

Correct answerYour answer

\int_1^{4} (6 - y)\,dy

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$R$ lies against the $y$ -axis, so use horizontal strips: at height $y$ a strip runs from $x = 0$ to $x = 6 - y$ .
The strips run from $y = 1$ to $y = 4$ : $\int_1^{4} (6 - y)\,dy$ .

Worth noting

$\int_0^{4} (6 - y)\,dy$ starts at the $x$ -axis, but the lower side of $R$ is the line $y = 1$ .

Concept: Integrating along \(y\)
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsRegions with lines

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