{"id":235283,"date":"2024-04-10T23:23:47","date_gmt":"2024-04-10T23:23:47","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=235283"},"modified":"2024-04-10T23:23:47","modified_gmt":"2024-04-10T23:23:47","slug":"how-to-do-integral-of-absolute-value","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-do-integral-of-absolute-value\/","title":{"rendered":"How to do integral of absolute value?"},"content":{"rendered":"

The integral of the absolute value function can be a bit tricky, but with the right approach, it can be calculated accurately. The absolute value function is defined as |x|, which represents the distance of a number x from zero on the number line. When integrating the absolute value function, it’s important to break it down into cases based on the sign of the argument. Here’s how to do the integral of the absolute value function step by step:<\/p>\n

1. **Case 1: x \u2265 0**
\n – When x is greater than or equal to zero, |x| simplifies to just x. So, the integral of |x|dx from 0 to a becomes \u222bx dx from 0 to a, which equals [x^2\/2] evaluated from 0 to a, giving us a^2\/2.<\/p>\n

2. **Case 2: x < 0**
\n – When x is less than zero, |x| simplifies to -x. So, the integral of |x|dx from -a to 0 becomes \u222b-x dx from -a to 0, which equals [-x^2\/2] evaluated from -a to 0, giving us a^2\/2.<\/p>\n

By following these steps and considering the different cases, you can easily calculate the integral of the absolute value function for any given interval.<\/p>\n

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