Where is 2x-1 ≥ 0 ?Mdhiggenz said:Homework Statement
∫[|2x-1|] evaluated on the interval [1,-1]
Homework Equations
The Attempt at a Solution
I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b]
and in absolute value one is negative and one is positive, so it will be
2x-1, and 1-2x my question is how do we know which interval to place each one in.
Do we place 1-2x in the interval from [c,b] or 2x-1, and vice versa,
thank you
That should allow you to evaluate [itex]\displaystyle \int_{-1}^1\ |2x-1|\,dx\,.[/itex]Mdhiggenz said:for 2x-1 when x is greater than or = to 1/2
and for 1-2x when x is less than or = to 1/2
?
The absolute value definite integral is a mathematical concept used to find the area between a function and the x-axis over a specific interval. It is represented by the symbol ∫|f(x)|dx and is calculated by taking the integral of the absolute value of the function over the given interval.
An absolute value definite integral differs from a regular definite integral in that it calculates the absolute value of the function before integrating, whereas a regular definite integral calculates the value of the function itself. This means that negative areas will be considered positive in an absolute value definite integral, whereas they would be negative in a regular definite integral.
An absolute value definite integral is necessary when the function being integrated has negative values and the area under the curve needs to be calculated without taking the direction of the y-axis into account. It is also useful when dealing with absolute values, such as in finding the distance traveled by an object with changing velocity.
To solve an absolute value definite integral, you first need to take the integral of the absolute value of the function over the given interval. Then, you can evaluate the integral by plugging in the upper and lower limits of the interval and taking the difference between the two values.
Absolute value definite integrals have many real-life applications, such as in calculating the total displacement of an object with changing velocity, finding the total work done by a varying force, and determining the total amount of material needed for a construction project with changing dimensions. They are also used in physics, engineering, and economics to solve various problems involving changing values.