Question

The area of the region bounded by the lines y = x + 1, x = 1, x = 3 and x-axis is

• A. 6 sq units
• B. 8 sq units
• C. 7.5 sq units
• D. 2 sq units

Answer 1

Answer: (A)

6 sq units

Answer 2

The area is found by integrating $y=x+1$ from $x=1$ to $x=3$. $\int_{1}^{3} (x+1) dx = \left[\frac{x^2}{2} + x\right]_{1}^{3} = \left(\frac{9}{2}+3\right) - \left(\frac{1}{2}+1\right) = \frac{15}{2} - \frac{3}{2} = 6 \text{ sq units}$ The region is a trapezoid with parallel sides 2 and 4, and height 2, yielding area $\frac{1}{2}(2+4)(2) = 6$ sq units.