$1.$ Evaluate the integral ${\displaystyle \underset{0}{\overset{}{}}}{e}^{-t}sin(t)dt.$ Clearly show your work using proper notation.

$(8$ points$)$

$2.$ The function $f(x)=x^{3}is$ shown below $in$ both graphs. For what value $oft>0$ will the

areas A and $Bbe$ the same? Clearly explain your process and evaluate all integrals $by$

hand. You may solve any equations using your calculator. Remember $to$ verify your

solution.

$(8$ points$)$

$3.$ What $is$ the value $of{\displaystyle \underset{1}{\overset{5}{}}}f(x)dxif{\displaystyle \underset{1}{\overset{5}{}}}(4f(x)-6)dx=36?$

$(4$ points$)$