When it comes to integrating the absolute value of x, you may find it challenging at first. The absolute value function |x| is defined differently for positive and negative values of x, so integrating it requires some extra steps. However, with the right approach, you can easily integrate the absolute value of x.<\/p>\n
To integrate the absolute value of x, you need to break it down into two separate cases: when x is positive and when x is negative. <\/p>\n
Here is how you can integrate the absolute value of x step by step:<\/p>\n
1. When x is positive: If x is positive, then |x| simplifies to just x. So the integral of |x|dx when x is positive is simply the integral of x dx. This can be solved by applying the power rule of integration.<\/p>\n
2. When x is negative: If x is negative, then |x| simplifies to -x. So the integral of |x|dx when x is negative is the integral of -x dx. Again, you can solve this by applying the power rule of integration.<\/p>\n
3. Combine the two cases: Finally, you can combine the results of the two cases to get the integral of the absolute value of x.<\/p>\n
4. The final result will be the piecewise function:
\n\u222b |x| dx =
\n1\/2 x^2 + C when x >= 0,
\n-1\/2 x^2 + C when x < 0.\n\n\nBy following these steps, you can integrate the absolute value of x without much difficulty.\n\n\n\n\n
How to integrate absolute value of x? When it comes to integrating the absolute value of x, you may find it challenging at first. The absolute value function |x| is defined differently for positive and negative values of x, so integrating it requires some extra steps. However, with the right approach, you can easily integrate … <\/p>\n