The area (in sq. units) of the region bounded by the line x − 2y = 4 and the coordinate axes is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
The line meets the x-axis at (4, 0) and the y-axis at (0, −2). Written as
\( \displaystyle y = \frac{x-4}{2} \)
it is below the x-axis for \(0 \le x \lt 4\), so the area is the integral of \(-y\):
\( \displaystyle A = \int_{0}^{4}\frac{4-x}{2}\,dx \)
\( \displaystyle = \left[2x-\frac{x^{2}}{4}\right]_{0}^{4} \)
\(= 8-4 = 4\)
The integral of y itself is −4; an area is never negative, so it is 4. The triangle with legs 4 and 2 gives \(\frac{1}{2}\times4\times2 = 4\) as well.