Set up an integral and compute the area of the enclosed regions below. You may use your graphing calculator.

1. The area between $y =\operatorname{sin }x$ and $y = (x − 1)^4 − 1$.

   Step 1 (a):

   Find the bounds by computing the $x$-values of the points of intersection between the two functions.
   $\operatorname{sin}x = (x −1)^4 −1$
   $a = 0$, $b = 2.163$ (using a calculator)

   Step 2 (a):

   Determine which is the upper function (the one with higher $y$-values) and which is the lower function (the one with lower $y$-values). If you are using a calculator: look at the graph. If not: Evaluate a point in between the bounds to see which function has the higher $y$-values.

2. The area between $y = x(x-3)$ and $y = \sqrt { x }$.

   Hint (b):

   Refer to hints in part (a).