The area (in sq. units) of the region bounded by the line joining the points (1, 1) and (3, 5), the x-axis and the lines x = 1 and x = 3 is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
The slope of the line is
\( \displaystyle m = \frac{5-1}{3-1} = 2 \)
so its equation is
\(y-1 = 2(x-1),\ \ y = 2x-1\)
For \(1 \le x \le 3\) we have y > 0, so the line is above the x-axis:
\( \displaystyle A = \int_{1}^{3}(2x-1)\,dx \)
\( \displaystyle = \left[x^{2}-x\right]_{1}^{3} = 6-0 = 6 \)