Determine the area bounded by the curve y = e^ -x , the X-axis and the Y-axis.

Step-by-step solution

The required area is bounded by the curve y = e^ -x , the X-axis ( y = 0 ) and the Y-axis ( x = 0 ). The area is given by the definite integral of the function from x = 0 to x = . A = ₀^ e^ -x dx A = [-e^ -x ]₀^ A = -(0 - 1) = 1