Which integral gives the area of the region bounded by $y = 3 - x$ and the two coordinate axes?

\int_0^{3} (x - 3)\,dx

Correct answerYour answer

\int_0^{3} (3 + x)\,dx

Correct answerYour answer

\int_{-3}^{3} (3 - x)\,dx

Correct answerYour answer

\int_0^{3} (3 - x)\,dx

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The line meets the axes at $(3, 0)$ and $(0, 3)$ , and lies above the $x$ -axis between them.
Area $= \int_0^{3} (3 - x)\,dx$ .

Worth noting

$\int_0^{3} (x - 3)\,dx$ subtracts the wrong way round and comes out negative.

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

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

Which integral gives the area of the region bounded by y=3−xy = 3 - xy=3−x and the two coordinate axes?