Need help for part 4 and 5. I figured out 1, 2, and 3.

In this question, we will compute the two integrals cas ( x ? )der = Him sin(x7 )dr = lim sin(2-)dr. At first glance it is not obvious that these integrals actually converge (i.e. that the limits as R -+ co exist), but we will prove this. We will need the following fact, which you may have seen before: (You do not need to prove this.) For now, we let R be a large positive real number (later we take R + co). We will integrate the function /(=) = e- along the closed curve consisting of three parts: . The real axis from 0 to R, . The 45" are from R to ()R, . The diagonal line from (1 ) R to 0. We refer to the three parts respectively by the names aris, are, diagonal. For example, we have A diagram of this closed curve is shown below. 1. Give a reason why the integral of f(2) around this curve is zero. 2. By finding a suitable parametrization of the diagonal part of the integral, show that Jangonal f(=)de = wa (cas(2 7 ) + sin(2 ? )de + (cos(1 7) - sin( 2 7 )da. So the diagonal integral is pretty close to what we actually want to compute. But in order to compare the diagonal integral to the axis integral, we need to control the arc integral. We parametrice the are in the following way. Let Y(t) = R. eit for 0