JEE Advanced 2022 Paper 2 Mathematics Q8

Mathematics

Problem

Consider the functions f,g:ℝ→ℝ defined by f(x)=x²+5/12 and g(x)=2(1−4|x|/3) for |x|≤3/4, while g(x)=0 for |x|>3/4. If α is the area of the region {(x,y)∈ℝ×ℝ:|x|≤3/4, 0≤y≤min{f(x),g(x)}}, then the value of 9α is _____________.

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