tjohn101 said:Yeah, I know. :) It's jut that it's worth 15 out of 100 points on our lab and our professor usually makes those questions the most difficult. It's unusual to have one so simple.
The function e^x, also known as the exponential function, is a mathematical function that is defined for all real numbers. It is commonly used to describe the growth or decay of quantities over time.
To find the area under the curve of e^x, you can use the integral calculus formula for finding the area under a curve. In this case, the formula would be ∫e^x dx, where the limits of integration would be from 0 to ln(9). You can use a calculator or computer software to evaluate this integral and find the area.
The interval [0,ln(9)] is a range of values for the independent variable x in the function e^x. In this case, the interval starts at 0 and ends at ln(9), which is approximately 2.197. This means that we are finding the area under the curve of e^x from x=0 to x=ln(9).
Specifying the interval is important because the function e^x is defined for all real numbers, so if we don't specify a specific range of values for x, we would be finding the area under the entire curve, which would be infinite. By specifying the interval, we are limiting the scope of our calculation to a finite area.
Finding the area under the curve of e^x can have several interpretations depending on the context. In general, it can represent the total change or growth of a quantity over a specific time period. In other cases, it can also represent the probability of a certain event occurring, or the amount of work done in a physical system. It is a fundamental concept in calculus and has many real-world applications.