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Definite Integration

JEE Main 2024 (Online) 31st January Evening Shift

MCQ+4 / -12024

Let \(f, g:(0, \infty) \rightarrow \mathbb{R}\) be two functions defined by \(f(x)=\int\limits_{-x}^x\left(|t|-t^2\right) e^{-t^2} d t\) and \(g(x)=\int\limits_0^{x^2} t^{1 / 2} e^{-t} d t\). Then, the value of \(9\left(f\left(\sqrt{\log _e 9}\right)+g\left(\sqrt{\log _e 9}\right)\right)\) is equal to :

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