How to solve an absolute value integral?

Thread starter physicsernaw
Start date May 5, 2013
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Absolute Absolute value Integral Value

In summary, the absolute value integral is a mathematical concept used to determine the total area under a curve on a graph, regardless of the sign of the function. It differs from a regular integral by taking into account both positive and negative areas, making it useful for finding total distance or change in a quantity. Its formula is similar to a regular integral, but with the absolute value of the function. Some practical applications include calculating displacement, profit, and work. The absolute value integral cannot be negative as it always results in a positive value or zero due to the absolute value property.

May 5, 2013

physicsernaw

Homework Statement

∫0-->x |t|dt

Homework Equations

The Attempt at a Solution

1/2*x^2 for x>= 0

1/2*(-x)^2 for x<= 0

Not sure what to do to be honest. (the answer in the back of the book says 1/2*x|x|).

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May 5, 2013

tiny-tim

Science Advisor

Homework Helper

hi physicsernaw!

(try using the X² button just above the Reply box

)

physicsernaw said:

1/2*(-x)^2 for x<= 0

how did you get that?

it should be -1/2 x²

Related to How to solve an absolute value integral?

1. What is the definition of absolute value integral?

The absolute value integral is a mathematical concept used to determine the area under a curve on a graph. It is similar to a regular integral, but instead of calculating the net area above and below the x-axis, it calculates the total area regardless of the sign of the function.

2. How is the absolute value integral different from a regular integral?

The main difference between the absolute value integral and a regular integral is that the absolute value integral takes into account both positive and negative areas, while a regular integral only considers the net area above or below the x-axis. This makes the absolute value integral useful for finding the total distance traveled or the total change in a quantity over a given time period.

3. What is the formula for calculating the absolute value integral?

The formula for calculating the absolute value integral is similar to the formula for a regular integral, but with the absolute value of the function being integrated. It can be written as:

∫|f(x)| dx = ∫f(x) dx, where f(x) is the function being integrated and dx represents the infinitesimal change in x.

4. What are some practical applications of the absolute value integral?

The absolute value integral has many practical applications in various fields such as physics, economics, and engineering. It can be used to calculate the total displacement or velocity of an object, the total profit or loss in a business, and the total work done by a force.

5. Can the absolute value integral be negative?

No, the absolute value integral cannot be negative. Since it calculates the total area, it will always result in a positive value or zero. This is because the absolute value of any number is always positive.