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Application of Integration question

2022 · Shift 2 · Q26

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PYQ Library
JEE Advanced
Mathematics
Application of Integration
2022 · Shift 2 · Q26

Application of Integration question

2022 · Shift 2 · Q26

JEE AdvancedMathematicsApplication of IntegrationNumerical+3 / −1

Consider the functions

f, g: \mathbb{R} \rightarrow \mathbb{R}

defined by

f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|\gt \frac{3}{4}\end{cases}

If

\alpha

is the area of the region

\left\{(x, y) \in \mathbb{R} \times \mathbb{R}:|x| \leq \frac{3}{4}, 0 \leq y \leq \min \{f(x), g(x)\}\right\},

then the value of

9 \alpha

is

Numerical answer

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