Find the shaded area between the given function and the x-axis.
A)

Question

Find the shaded area between the given function and the x-axis. ​   ​
A) ​

Quizplus · Accepted Answer

The shaded area is bounded by the x-axis and the curve y = e^x + 1. To find the area, we integrate this curve with respect to x over the interval from x = 0 to x = ln(2), where the curve intersects the x-axis:

integral from 0 to ln(2) of (e^x + 1) dx = e^x + x |_0^ln(2) = (e^ln(2) + ln(2)) - (e^0 + 0) = 2 + ln(2)

Therefore, the shaded area is approximately 2.693. Choice B is the closest to this value.

Find the Shaded Area Between the Given Function and the X-Axis