Question

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

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

Answer 1

Answer: (B)

(B) 4 sq. unit

Answer 2

Explanation:
Given curve and lines are:y=x−2 and x=0 to x=4In figure △ABC and △AOD is similar.So, Area of the region =2×( Area of △ABC)For the area of △ABCWe know that:=∫x1x2|y2−y1|dx=∫24(x−2)dx=[x22−2x]24=422−2(4)−(222−2×2)=8−8−2+4=2 sq. unitSo, Area of the region =2×( Area of △ABC)=2×2=4 sq. unitHence, the correct option is (B).