Generally.
Area = the definite integration from a to b [ f(x) - g(X)]dx
Say you have two functions( y = e^x and y = x) and you want to find the area between them on an interval ( say 1 to 3 ) So you set the top function(e^x) subtracting the bottom function(x) and integrate them, Insert the values, b - a in the integrated functions and get the value of the area.
If the values of the function are all positive, then the integral IS the area under the curve.
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
Do a line integral.
Finding the area under a curve or the length of a line segment. These are real life uses, not just fun in your math class.
The distance covered between two points in time is the area under the graph between the two points.
Integration can be used to calculate the area under a curve and the volume of solids of revolution.
The area under the standard normal curve is 1.
If this is on mymaths.co.uk then the answer to this question is: Integration. That is how to find the area under the curve.
The area under the normal curve is ALWAYS 1.
Basically this isn't possible. Whenever you have an irregular curve, you need some kind of integration technique to get the area, or an estimate of the area. This can be quite simple, at least in principle: just approximate the area by narrow rectangles, calculate the area of each rectangle, and add everything up.
If the values of the function are all positive, then the integral IS the area under the curve.
There is no histogram below.However, the area under the curve for any histogram is the total frequency.
the standard normal curve 2
WORK
if its a mathematical curve, say v=10t - t^2 (from t = 1 to 5), using calculus, you can calculate instant acceleration (slope of the tangent of the curve at any point) by differentiation, or distance travelled over a time interval (area under graph) by integration. if its say data driven, you can approximate slope and area
What is the area under the normal curve between z=0.0 and z=1.79?
The area under the normal distribution curve represents the probability of an event occurring that is normally distributed. So, the area under the entire normal distribution curve must be 1 (equal to 100%). For example, if the mean (average) male height is 5'10" then there is a 50% chance that a randomly selected male will have a height that is below or exactly 5'10". This is because the area under the normal curve from the left hand side up to the mean consists of half of the entire area of the normal curve. This leads us to the definitions of z-scores and standard deviations to represent how far along the normal curve a particular value is. We can calculate the likelihood of the value by finding the area under the normal curve to that point, usually by using a z-score cdf (cumulative density function) utility of a calculator or statistics software.