Definite Integral

A definite integral is an integral that has both a lower and an upper limit. A definite integral is expressed as:

Definite Integral - 2.png

In this case, is the lower limit, and b is the upper limit of the integral. This can be modeled graphically as:

Definite Integral - 1.png

To solve a definite integral, you take the antiderivative of the function and evaluate the antiderivative at its upper limit and subtract it from the antiderivative evaluated at the lower limit. Expressed mathematically:

Definite Integral - 3.png

When computing an antiderivative, you create a family of equations, which is why you add a constant to the antiderivative. However, when solving a definite integral that is not only not necessary, but is incorrect to do so. The reason for this is because we are subtracting the lower limit from the upper limit, and since they would have the same constant value it cancels itself out.