What are the units for area under the curve?

The units of the AUC are the units of the Y axis times units of the X axis. For example, if your Y axis measures concentration in mmol/L and the X axis measures time in minutes, then the area is expressed in units of (mmol/L) x minutes.

What is the area under the curve equal to?

The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be calculated using integration with given limits.

What does the area under the curve represent math?

Then the area under the whole curve is just the sum of the areas of all these tiny rectangles under the curve. Should you be interested in finding out more about this it is called Riemann integration. And velocity v times time dt is just the distance moved at a velocity v in a time dt. So the area is a distance moved.

What is the area under a derivative curve?

The derivative can give you a precise intantaneous value for that rate of change and lead to precise modeling of the desired quantity. The integral of a function can be geometrically interpreted as the area under the curve of the mathematical function f(x) plotted as a function of x.

What does area under the curve mean in pharmacokinetics?

From Wikipedia, the free encyclopedia. In the field of pharmacokinetics, the area under the curve (AUC) is the definite integral of a curve that describes the variation of a drug concentration in blood plasma as a function of time (this can be done using liquid chromatography–mass spectrometry).

What does it mean when you calculate the area under a curve and obtain a value that is negative?

The area under a curve between two points can be found by doing a definite integral between the two points. Areas under the x-axis will come out negative and areas above the x-axis will be positive. This means that you have to be careful when finding an area which is partly above and partly below the x-axis.

Why would you want to find the area under a curve?

Originally Answered: Why is it important to know the area of a curve in integral calculus? The area under a curve will indicate a number directly related to the data. Depending on the problem you are solving, it will be a solution to a question.

How do you find the area of Y = eX?

Start by finding the intersection point of the two functions. We also know through end behaviour of the function that y = ex will be above y = e−x. So, we determine the area of y = ex in the interval 0 ≤ x ≤ 1 and then subtract the area of y = e−x in the interval 0 ≤ x ≤ 1. This can be approximated to 1.086 u2.

How do you find the area under a curve in math?

Area Under the Curve Formula. The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b.

Can the area under a curve be negative?

This is not the correct answer for the area under the curve. It is the value of the integral, but clearly an area cannot be negative. It’s always best to sketch the curve before finding areas under curves.

Why does the area under a curve become the anti-derivative?

However when it comes to the area under a curve for some reason when you break it up into an infinite amount of rectangles, magically it turns into the anti-derivative. Can someone explain why that is the definition of the integral and how Newton figured this out?