CPM Homework Help : APCALC Problem 4-164

Set up an integral and compute the area of the region bounded by the graphs of the given functions. You may use a graphing calculator.

Calculator OK

The area between $y=\sin\left(x\right)$ and $y = \left(x – 1\right)^{4} – 1$ .
Hint (a):
$\text{Area between curves }=\int_{a}^{b}\text{(upper fuction) - (lower function)}dx$
Step 1(a):
Find the bounds by computing the $x$ -values of the points of intersection between the two functions.
$\sin x=\left(x−1\right)^4−1$
$a = 0, b = 2.163$ (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.
The area between $y = x\left(x – 3\right)$ and $y=\sqrt{x}$ .
Hint (b):
Refer to hints in part (a).