Problem: Consider the following integral:$I(x) = \int_0^{π/4}\sqrt{sin (t)}e^{-x^2t^2}dt$ In the limit$x \rightarrow \infty$, find approximate behavior of the integral up to and including the leading order in x. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(x) = \frac{1}{2}x^{-3/2}\cdot\Gamma(\frac{3}{4})}$