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Where you refer to a particular integral I will assume you mean a definite integral. To illustrate why there is no constant of integration in the result of a definite integral let me take a simple example. Consider the definite integral of 1 from 0 to 1. The antiderivative of this function is x + C, where C is the so-called constant of integration. Now to evaluate the definite integral we calculate the difference between the value of the antiderivative at the upper limit of integration and the value of it at the lower limit of integration: (1 + C) - (0 + C) = 1 The C's cancel out. Furthermore, they will cancel out no matter what the either antiderivatives happen to be or what the limits of integration happen to be.
The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.
First, find the area under the curve y = 1/x2, with boundary lines x = 1 and x = 6, by calculating the integral of 1/x2 with lower limit 1, and upper limit 6. Then divide it by 2. (6)integral(1) of (1/x2) dx = (6)integral(1) of (x--2) dx = -x-1|(6),(1) = -1/x|(6)(1) = -1/6 +1 = 5/6. Thus, the half of the area under the curve is 5/12.
You could find an inclined plane in a skate park because of all the ramps.
38; 39; 40!