An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value or quantity of a function over a given interval.
To solve an integral, you need to use integration techniques such as substitution, integration by parts, or trigonometric substitution. You also need to know the limits of integration, which represent the interval over which you are finding the area.
The absolute value in an integral represents the distance from the x-axis. In the case of this integral, the absolute value of x means that the function will be positive for all values of x, regardless of whether x is positive or negative.
The step-by-step solution to this integral involves breaking it into two separate integrals based on the limits of integration. For the interval [-1,0], the integral of x - 2|x| is equal to (-x^2/2) - (2x^2/2) + C. For the interval [0,2], the integral of x - 2|x| is equal to (x^2/2) - (2x^2/2) + C. Combining these two solutions gives the final solution of x^2 - 2|x|^2 + C.
This integral can be considered easy to solve for those who are familiar with integration techniques. However, for those who are new to integrals, it may require some practice and understanding of the concepts involved. It is always helpful to break the integral into smaller parts and use a step-by-step approach to find the solution.