If $f\,\,\left( x \right) = \mathop \smallint \nolimits_{{x^2}}^{{x^2} + 1} \,\,{e^{ - {t^2}}}\,dt$, then $f\,\,\left( x \right)$ increases in

$\left( {0,\;\,\,\infty } \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

f\,\,\left( x \right) = \int \nolimits_{{x^2}}^{{x^2} + 1} \,\,{e^{ - {t^2}}}\,dt

, then

f\,\,\left( x \right)

increases in

View answer and explanation

Correct option: D

\left( { - \,\infty ,\;\,0} \right)

Option D ((

- \,\infty ,\;\,0

)) is correct because the derivative of the function is positive when x < 0, indicating that the function is increasing in that interval.

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