How to Calculate An Integral Defined
Math, you know, is a complex and articulated. And one of the arguments more difficult to study are undoubtedly integrals. Solve an integral means to calculate the area under the function (usually represented by a curve) taken into consideration, which is the area between the graph of the curve and the x-axis (x). There are different types of grains, but today we will deal with those “defined”. The definite integral is calculated between a precise interval [a, b], in which we imagine to be able to “split” the area into small rectangles, so small as to be considered rectangles having intervals of zero measure. Now let’s see How to Calculate An Integral Defined.
An integral is represented by the formula opposite: the extremes of the interval are marked at the two sides (top and bottom) of the symbol, while inside of it is described the function and the variable in which the latter has to be integrated. To solve a definite integral must first use the classic formulas of integration; then the function F (x) obtained will be evaluated in the two extremes and b, so as to be able to calculate the difference F (b) – F (a). In other words, once you got the indefinite integral, we must replace the integration variable (in our case, x) the value “b” and then the value “a”. However, in spite of the letters present, remember that a definite integral is a measure, then a number. The technique of integration by parts is very useful in particular in the resolution of the products between two functions that would otherwise be very difficult. If you are familiar with the derivatives, know that the calculation of an integral is the inverse of that for the derivatives.
This means that after calculating the integral of a function, the integrated function is nothing but the derivative of the result of the integral, which is called ” primitive integral “. In other situations, the integral can be reduced to an integral remarkable, that it will be possible to derive from any mathematical form. For example, we describe some trigonometric functions: the integral of the function cos (x) is equal to sin (x), while that of sin (x) is -cos (x). In other more complex cases you can make use of so-called rules of integration, or the technique of integration by parts. In some fields, especially related to physics and electronics, is also very useful technique of integration by substitution, which allows to turn the function in another note by a change of variable of integration.