Question

Find the area between the curve y=x2 and y=x.

• A. (A) 56 sq. unit
• B. (B) 13 sq. unit
• C. (C) 12 sq. unit
• D. (D) 16 sq. unit

Answer 1

Answer: (D)

(D) 16 sq. unit

Answer 2

Explanation:
Given:Curve 1:y=x2=f(x) (say)Curve 2 : y−x=0⇒y=x=g(x) (say)The curve can be drawn as:To find the intersections (or limits of the area) putting value of y from curve 1⇒x2−x=0⇒x(x−1)=0⇒x=0,x=1Now the required area (A) is:A=|∫x1x2[f(x)−g(x)]dx|⇒A=|∫01[x2−x]dx|⇒A=|[x33−x22]01|⇒A=|13−12−(0)|⇒A=16 sq. unitHence, the correct option is (D).