Let f, g:(0, ∞) → R be two functions defined by f(x)=∫ -x ˣ(|t|-t²) e^(-t²) d t and g(x)=∫₀^(x²) t^(1 / 2) e^(-t) d t. Then, the value of 9(f(√(log e 9))+g(√(log e 9))) is equal to:

Integral Calculus: JEE Main 2024 Mathematics question

JEE Main 2024 · 31 Jan, Evening shift · Q3473

JEE Main 202431 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

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 :

JEE Main 2024 Integral Calculus Question with Solution (31 Jan Evening shift, Q3473) | JEE Arc

JEE Main 2024 · 31 Jan, Evening shift · Q3473

JEE Main 202431 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

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 :