Question

What is the area of the parabola x2=y bounded by the line y=1?

• A. (A) 13 square unit
• B. (B) 23 square unit
• C. (C) 43 square units
• D. (D) 2 square units

Answer 1

Answer: (C)

(C) 43 square units

Answer 2

Explanation:
Concept:The area under the curve y=f(x) between x=a and x=b, is given by: Area =∫abydxCalculation:Here,x2=y and line y=1 cut the parabola∴x2=1⇒x=1 and −1Area =∫−11ydxHere, the area is symmetric about the y-axis, we can find the area on one side and then multiply it by 2, we will get the area,Area 1=∫01ydxArea 1=∫01x2dx=[x33]01=13This area is between y=x2 and the positive x-axis.To get the area of the shaded region, we have to subtract this area from the area of square i.e.(1×1)−13=23Total Area =2×23=43 square units.Hence, the correct option is (C).