Question:
Let a, b be positive real numbers such that \(a\lt b\). Given that
\(\lim\limits_{N\rightarrow\infin}\displaystyle\int^{N}_{0}e^{-t^2}dt=\frac{\sqrt \pi}{2},\) the value of
\(\lim\limits_{N\rightarrow\infin}\displaystyle\int^{N}_{0}\frac{1}{t^2}(e^{-at^2}-e^{-bt^2})dt\) is equal to
Let a, b be positive real numbers such that \(a\lt b\). Given that
\(\lim\limits_{N\rightarrow\infin}\displaystyle\int^{N}_{0}e^{-t^2}dt=\frac{\sqrt \pi}{2},\) the value of
\(\lim\limits_{N\rightarrow\infin}\displaystyle\int^{N}_{0}\frac{1}{t^2}(e^{-at^2}-e^{-bt^2})dt\) is equal to
\(\lim\limits_{N\rightarrow\infin}\displaystyle\int^{N}_{0}e^{-t^2}dt=\frac{\sqrt \pi}{2},\) the value of
\(\lim\limits_{N\rightarrow\infin}\displaystyle\int^{N}_{0}\frac{1}{t^2}(e^{-at^2}-e^{-bt^2})dt\) is equal to
Updated On: Jan 30, 2025
- √π(√a – √b).
- √π(√a + √b).
- -√π(√a + √b).
- √π(√b – √a).
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The Correct Option is D
Solution and Explanation
The correct option is (D): √π(√b – √a)
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