zeezey said:The Attempt at a Solution
So I the area should be integral of e^x - 2 which = e^x - 2x . I'm not sure what to do with the y-axis it mentions?
The "area between two curves problem" is a mathematical concept that involves finding the area between two curves on a graph. This problem is typically encountered in calculus, and it requires the use of integration to find the area between the curves.
To solve the "area between two curves problem", you must first identify the two curves and the interval over which you want to find the area. Then, you can use the integration formula to find the area between the curves. This involves finding the antiderivative of the difference between the two curves and evaluating it at the upper and lower bounds of the interval.
The "area between two curves problem" has many real-life applications in fields such as engineering, physics, and economics. For example, it can be used to calculate the area under a velocity-time graph to determine the displacement of an object, or to find the profit or loss between two different business strategies.
Yes, there are several special cases to consider when solving the "area between two curves problem". One common exception is when the two curves intersect multiple times within the given interval. In this case, you would need to break up the interval into smaller intervals and calculate the area separately for each interval.
One helpful tip for solving the "area between two curves problem" efficiently is to carefully sketch the two curves on a graph to visually understand the problem. This can also help you identify any special cases or exceptions that may arise. Additionally, it is important to pay attention to the bounds of the interval and double check your work to ensure accuracy.