code class$=$"asciimath"$>1(6$ pts$.)$ Evaluate the integral using series $($Hint $($:$sinx={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n{x}^{2n+1}}{(2n+1)!}\},$ leaving your answer as a series: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sin2x^{2}dx(6$ pes.$)$ Find the mediton $M$ of anrz exponerrtially distributed raxidom variable with pdf $f(x)=\{\begin{array}{cc}0,& x<0\\ 0-cx,& x0\end{array}$ Recall that the median divides the ares under a PDF into two equal halvos $($of area one$-$hall$).$ So an equation to solve for $M$ mighe be: $\frac{}{2}={\displaystyle \underset{-}{\overset{ns}{}}}f(x)dx={\displaystyle \underset{0}{\overset{\phantom{}}{}}},$ since for the given PDF $f(x)=0$ for $x<0.$ Show your work. $(6$ pes.$)$ Find the mediton