Jee Advanced
Definite Integration
JEE Advanced 2021 Paper 2 Online
MCQ+3 / -12021
Let \({\psi _1}:[0,\infty ) \to R\), \({\psi _2}:[0,\infty ) \to R\), f : (0, \(\infty\)) \(\to\) R and g : [0, \(\infty\)) \(\to\) R be functions such that f(0) = g(0) = 0,
\({\psi _1}(x) = {e^{ - x}} + x,x \ge 0\),
\({\psi _2}(x) = {x^2} - 2x - 2{e^{ - x}} + 2,x \ge 0\),
\(f(x) = \int_{ - x}^x {(|t| - {t^2}){e^{ - {t^2}}}dt,x > 0}\) and
\(g(x) = \int_0^{{x^2}} {\sqrt t {e^{ - t}}dt,x > 0}\).
\({\psi _1}(x) = {e^{ - x}} + x,x \ge 0\),
\({\psi _2}(x) = {x^2} - 2x - 2{e^{ - x}} + 2,x \ge 0\),
\(f(x) = \int_{ - x}^x {(|t| - {t^2}){e^{ - {t^2}}}dt,x > 0}\) and
\(g(x) = \int_0^{{x^2}} {\sqrt t {e^{ - t}}dt,x > 0}\).
Which of the following statements is TRUE?