The area of the region bounded by the curve y=e^-x, the x-axis, the y-axis, and the line x=2 is equal to

Question

The area of the region bounded by the curve y=e^-x, the x-axis, the y-axis, and the line x=2 is equal to

Answer 1

1) Graph the y = e^-x function (can use an xy-table by choosing x-values such as -2, -1, 0, 1, and 2 and plugging them into the function to find y

2) Draw a vertical line down from the graphed function to the x-axis at x = 2 because the function is bounded here

3) shade in the region under the curve, above the x-axis, and between x = 0 and x = 2 because the function is bounded by these points

4) take the antiderivative of e^-x evaluated from x = 0 to x = 2