If $f\left( t \right) = \mathop \smallint \nolimits_{ - t}^t \,\,\frac{{{e^{ - \left| x \right|}}}}{2}\,\,dx,\;\,\,{\rm{then}}\,\,\mathop {\lim }\limits_{t \to \infty } \,\,f\,\,\left( t \right)$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

f\left( t \right) = \int \nolimits_{ - t}^t \,\,\frac{{{e^{ - \left| x \right|}}}}{2}\,\,dx,\;\,\,\mathrm{then}\,\,\lim\limits_{t \to \infty } \,\,f\,\,\left( t \right)

is equal to

View answer and explanation

Correct option: A

\mathrm{1}

Option A (1) is correct because the limit of the integral as t approaches infinity is 1 after evaluating the integral and applying the limit.

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