CPM Homework Help : CALC3RD Problem 5-85

Use your calculator to estimate the shaded area shown between the graphs of $y = 4 – 2\left(x – 2\right)^{2}$ and $y = 2^{x}$ .

Downward parabola, vertex at (2, comma 4), intersects increasing exponential curve at (1, comma 2), (2, comma 4), region below parabola, above curve, & between intersection points shaded.

Step 1:

Identify where the functions intersect, as well as which function is 'greater' (has higher $y$ -values) than the other.

Step 2:

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