Final answer:
To find the area of the region bounded by the curve y=eˣ, y-axis, and y=e², you can calculate the area between the curve and the x-axis, the y-axis, a horizontal line, and a vertical line.
Step-by-step explanation:
To find the area of the region bounded by the curve y=eˣ, y-axis, and y=e², we can calculate the area between:
a) The curve and the x-axis: This is the area under the curve y=eˣ. To find this area, we can integrate the function from the x-values where the curve intersects the x-axis.
b) The curve and the y-axis: This is the area to the left of the curve y=eˣ. To find this area, we can integrate the function from the y-value where the curve intersects the y-axis.
c) The curve and a horizontal line: To find the area between the curve and a horizontal line, we can subtract the y-values of the points where the curve intersects the line and integrate the function between those x-values.
d) The curve and a vertical line: To find the area between the curve and a vertical line, we can subtract the x-values of the points where the curve intersects the line and integrate the function between those y-values.