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If $f (x) = \int_{x^{2}}^{x^{2} + 4} e^{- t^{2}} d t,$ then the function $f (x)$ increases in

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detailed solution

Correct option is A

f′(x)=2xe−x2+42−2xe−x4=2xe−x2+421−e16+8x2Since 1−e16+8x2<0¯ for all x so f increases for x<0.

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If f(x)=∫x2x2+4 e−t2dt, then the function f(x) increases in

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If $f (x) = \int_{x^{2}}^{x^{2} + 4} e^{- t^{2}} d t,$ then the function $f (x)$ increases in