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Definite Integration question

2022 · 24 Jun · Shift 1 · Q41

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 24 Jun · Shift 1 · Q41

Definite Integration question

2022 · 24 Jun · Shift 1 · Q41

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

\mathop {Max}\limits_{0\, \le x\, \le 2} \left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \alpha

and

\mathop {Min}\limits_{0\, \le x\, \le 2} \left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \beta

. If

\int\limits_{\beta - {8 \over 3}}^{2\alpha - 1} {Max\left\{ {{{9 - {x^2}} \over {5 - x}},x} \right\}dx = {\alpha _1} + {\alpha _2}{{\log }_e}\left( {{8 \over {15}}} \right)}

then

{\alpha _1} + {\alpha _2}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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