How Do You Integrate sqrt(|x|) for Different Values of x?

Thread starter ahmed39399
Start date Mar 22, 2010
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Absolute Absolute value Integrate Value

In summary, the absolute value of a number is its distance from 0 on the number line and is always a positive number. Integrating absolute value is important because it allows us to find the area under a curve with both positive and negative values, and helps us solve problems involving displacement and distance. The general formula for integrating absolute value is ∫|f(x)|dx = ∫f(x)dx when f(x) ≥ 0 and ∫|f(x)|dx = -∫f(x)dx when f(x) < 0. An example of integrating absolute value is finding the area under the curve y = |x| from x = -2 to x = 2, which is 8 square units.

Mar 22, 2010

ahmed39399

How we can integrate this (without integration limits)

sqrt (|x|)

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Mar 22, 2010

Mark44

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ahmed39399 said:

How we can integrate this (without integration limits)

sqrt (|x|)

Use two different cases: when x >= 0, and when x < 0.

FAQ: How Do You Integrate sqrt(|x|) for Different Values of x?

What is the definition of absolute value?

The absolute value of a number is its distance from 0 on the number line. It is always a positive number.

Why is it important to integrate absolute value?

Integrating absolute value allows us to find the area under a curve that has both positive and negative values. It also helps us solve problems involving displacement and distance.

What is the general formula for integrating absolute value?

The general formula for integrating absolute value is: ∫|f(x)|dx = ∫f(x)dx when f(x) ≥ 0 and ∫|f(x)|dx = -∫f(x)dx when f(x) < 0.

Can you give an example of integrating absolute value?

Sure, let's say we want to find the area under the curve y = |x| from x = -2 to x = 2. We can break this into two integrals: ∫-2^02 x dx, which is equal to 4, and ∫02 x dx, which is also equal to 4. Therefore, the total area under the curve is 8 square units.

What are some real-life applications of integrating absolute value?

Integrating absolute value is commonly used in physics and engineering to solve problems involving displacement, velocity, and acceleration. It is also used in economics to calculate consumer and producer surplus. Additionally, it can be used in statistics to find the area under a normal distribution curve.