Changes

==Anti-derivative==

==Anti-derivative==

Most students struggle with the important difference between the anti-derivative and intergration. The anti-derivative of a function <math>f(x)</math> is the function <math>g(x)</math> such that,

Most students struggle with the important difference between the anti-derivative and integration. The anti-derivative of a function <math>f(x)</math> is the function <math>g(x)</math> such that,

<math>\frac{d}{dx}g(x)=f(x)</math>

<math>\frac{d}{dx}g(x)=f(x)</math>

The intergral of a function can be evaluated using its antiderivative,

The integral of a function can be evaluated using its antiderivative,

<math>\int_a^b f(x)dx=g(b)-g(a)</math>

<math>\int_a^b f(x)dx=g(b)-g(a)</math>

<math>\int^\infty_{-\infty} f(x)=g(x)+C</math>

<math>\int^\infty_{-\infty} f(x)=g(x)+C</math>

In the second case C is the constant of intergration. As this is very common <math>\infty</math> and <math>-\infty</math> are usually excluded. This works for the kind of functions incountered in late high school and early univeristy mathematics it is however an incomplete method. For example <math>e^{x^{2}}</math> has no anti-derivative.

In the second case C is the constant of integration. As this is very common <math>\infty</math> and <math>-\infty</math> are usually excluded. This works for the kind of functions incountered in late high school and early university mathematics it is however an incomplete method. For example <math>e^{x^{2}}</math> has no anti-derivative.

==Riemann intergral==

==Riemann intergral==

As a geometric interpretation of the integral of the area of a curve the Riemann integral consist of dividing the area under the curve of the function into rectangles.

As a geometric interpretation of the integral of the area of a curve the Riemann integral consist of dividing the area under the curve of the function into rectangles.

==Labegue Intergral==

==Lebesgue Intergral==

==See Also==

==See Also==