Question

Find the area of the region (in square unit) bounded by the curve $y=x-2$ and $x=0$ to $x=4$.

• (A) 2 sq. unit
• (B) 4 sq. unit
• (C) 3 sq. unit
• (D) 6 sq. unit

Answer 1

The Correct Option is B

Explanation:
Given curve and lines are:$y=x-2$ and $x=0$ to $x=4$

In figure $\mathrm{△}\mathrm{ABC}$ and $\mathrm{△}\mathrm{AOD}$ is similar.So, Area of the region $=2\times ($ Area of $\mathrm{△}\mathrm{ABC})$For the area of $\mathrm{△}ABC$We know that:$={\int }_{{\mathrm{x}}_1}^{{\mathrm{x}}_2}|{\mathrm{y}}_2-{\mathrm{y}}_1|\mathrm{dx}$$={\int }_2^4(\mathrm{x}-2)\mathrm{dx}$$={[\frac{{\mathrm{x}}^2}{2}-2\mathrm{x}]}_2^4$$=\frac{4^2}{2}-2(4)-(\frac{2^2}{2}-2\times 2)$$=8-8-2+4$$=2$ sq. unitSo, Area of the region $=2\times ($ Area of $\mathrm{△}\mathrm{ABC})$$=2\times 2$$=4$ sq. unitHence, the correct option is (B).