Final answer:
To find the area of the region bounded by the curves y = eˣ - 5 and y = sin(x), we need to find the points of intersection and integrate the difference between the curves.
Step-by-step explanation:
To find the area of the region bounded by the curves y = eˣ - 5, y = sin(x), x = 1, and x = ?, we need to find the points of intersection of the curves. The curves intersect when eˣ - 5 = sin(x), which can be solved numerically using a graphing calculator or software.
Once we find the x-values of the points of intersection, we can find the area by integrating the difference between the curves.
Let's assume for example that we find the x-values of the points of intersection to be x = 2 and x = 4. We can then integrate the difference between the curves from x = 1 to x = 4: ∫(eˣ - 5 - sin(x)) dx. Evaluating this integral will give us the area of the region bounded by the curves.