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

• A. √π(√a – √b).
• B. √π(√a + √b).
• C. -√π(√a + √b).
• D. √π(√b – √a).

Answer 1

The Correct Option is D

The correct option is (D): √π(√b – √a)