CPM Homework Help : APCALC Problem 5-28

Calculate the area between the curves $y=\sin\left(\pi x\right)$ and $y = x^{2} – 3x$ .

Step 1:

Use your calculator to find the points of intersection between the two graphs.
Then determine which graph is on top (has higher $y$ -values) and which is below.

Graph:

Upward parabola, labeled the quantity, x minus 3 times x, vertex at the point (1.5, comma negative 2.25), & periodic curve, labeled sine of pi x, from x values negative 10 to 10, with 20 visible turning points, oscillating between y = negative 1 & y = 1.

Step 2:

$\text{integrate:}\int_{\text{intersection }A}^{\text{intersection }B}([\text{top function}]-[\text{bottom function}])dx$

Answer:

$5.137$ units²