Definite Integration

MathsDirect

Imagine a curve, whose gradient is given by

To find the difference in y, between x=1 and x=4, you would first need to integrate
When x=1
and when x=4
The change in y is, therefore		Notice that the unknown constant has vanished.
When you find the difference between an integral at 2 values of x, you can ignore the constant and are left with a number.
This is called Definite Integration.
If you are going to evaluate a definite integral, you need to specify limits. That is, you need to give 2 values of x to integrate between. You give these limits, by writing the values at the top and bottom of the integral sign. The example above is written:		The result of the integration is written in square brackets, with the limits to the right. You then substitute the limits into the integral, the top limit first. Write the 2 parts in curly brackets, to keep the separate. Once you have worked these out, subtract the second bracket from the first.

If you study the following examples, the process should become clear.

Integrate 2x+3, between 0 and 5.

Evaluate the following definite integral.		The terms are first written in the form ln1=0 ln 4 = ln 2² = 2 ln 2

Evaluate the following definite integral		Note that the result of definite integrals can be negative.

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