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Question

Question: The area of the region {(x, y) : x<sup>2</sup>£ y £ \|x\|} is –...

The area of the region {(x, y) : x2£ y £ |x|} is –

A

1/3 sq. units

B

1/2 sq. units

C

1/4 sq. units

D

None of these

Answer

1/3 sq. units

Explanation

Solution

Hence, the required region R is the shaded region shown in figure. Since both the curves are symmetrical about y-axis. So, required area = 2(Shaded area in first quadrant)

= 201(xx2)dx=2×16=13\int _ { 0 } ^ { 1 } \left( x - x ^ { 2 } \right) d x = 2 \times \frac { 1 } { 6 } = \frac { 1 } { 3 }sq. units.