Final answer:
The area between the curve y = -e^-x and y = 0 is 0. The correct answer is c) 0.
Step-by-step explanation:
To find the area between the curve y = -e^-x and y = 0, we need to determine the points of intersection between the curve and the x-axis.
Setting y = 0 in the equation -e^-x = 0:
e^-x = 0
There are no solutions to this equation, which means the curve does not intersect the x-axis. Therefore, the area between the curve and the x-axis is 0.
The question asks us to find the area between the curve y = -e-x and the line y = 0. To find this area, we would typically integrate the absolute value of the function between the bounds where the function crosses the y=0 line. However, since the exponential function never touches the x-axis (y=0 line), the area under the curve from negative to positive infinity would theoretically be infinite.
In this specific case, the function is negative (y = -e-x), which reflects it below the x-axis, and when you're asked to find the 'area between the curve and y=0', you're typically interested in the absolute area which should be positive, even if the function lies below the x-axis.
The exponential function e-x approaches 0 as x approaches positive infinity and approaches positive infinity as x approaches negative infinity. Even though the function is multiplied by a negative sign, the area under the curve remains positive since area cannot be negative.