The area (in square units) of the region bounded by the curves y + 2x^2 = 0 and y + 3x^2 = 1, is equal to

JEE Main 2015 Mathematics question

The area (in square units) of the region bounded by the curves and , is equal to

(1) sq. units
(2) sq. units
(3) sq. units
(4) sq. unitsCorrect

Answer: (4)

Solution

Write the curves as (a downward parabola through the origin) and (a downward parabola with vertex ). They meet where , i.e. , so . Between these limits , since the difference is $1 -

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Question ID VK-115308