TS EAMCET · Maths · Definite Integration
If \(f(t)=\int_{-t}^t \frac{e^{-|x|}}{2} d x\), then \(\lim _{t \rightarrow \infty} f(t)\) is equal
- A \(1\)
- B \(\frac{1}{2}\)
- C \(0\)
- D \(-1\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} f(t) & =\int_{-t}^t \frac{e^{-|x|}}{2} d x \\ & =2 \int_0^t \frac{e^{-x}}{2} d x \\ & =-\left[e^{-x}\right]_0^t=-e^{-t}+1\end{aligned}\) Now,…
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