Question

The area bounded by $y=x-1$, $1\le x\le 2$, $y=0$ (in sq.units) is

• A. 2
• B. 1
• C. $\frac{1}{2}$
• D. 4
• E. $\frac{1}{4}$

Hint:

This area is a triangle with base 1 ($2-1$) and height 1 ($f(2)$). Area $= 1/2 \times 1 \times 1 = 1/2$.

Answer 1

The Correct Option is C

Step 1: Concept
Area $= \int_{a}^{b} y dx$.

Step 2: Analysis
Area $= \int_{1}^{2} (x-1) dx$.

Step 3: Calculation
$[\frac{x^2}{2} - x]_{1}^{2} = (\frac{4}{2} - 2) - (\frac{1}{2} - 1)$ $= 0 - (-1/2) = 1/2$. Final Answer: (C)