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Fermat1
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How would I compute the following integral? Let t be in [0,1].
$\int_{0}^{t}|s-t|\,ds$
$\int_{0}^{t}|s-t|\,ds$
Fermat said:How would I compute the following integral? Let t be in [0,1].
$\int_{0}^{t}|s-t|\,ds$
The integral is for s from 0 to t so s is always less than t and s- t is always negative. |s- t|= -(s- t) soFermat said:How would I compute the following integral? Let t be in [0,1].
$\int_{0}^{t}|s-t|\,ds$
The integral of |s-t| is used to calculate the absolute difference between two variables, s and t. It is commonly used in mathematics and physics to measure the distance between two points.
To compute the integral of |s-t|, you first need to determine the limits of integration, which in this case are 0 and t. Then, you need to write the integrand as |s-t| and include the differential "ds" at the end. This will give you the setup for the integral: ∫0t|s-t|ds
The steps to solve the integral of |s-t| are as follows:
Sure, let's say we want to compute ∫03|s-2|ds. First, we set up the integral: ∫03|s-2|ds. Then, we integrate the absolute value function, which gives us two cases: ∫02(2-s)ds + ∫23(s-2)ds. Solving these two integrals, we get 2 + 1 = 3. Therefore, the final answer is 3.
The integral of |s-t| has many real-life applications, such as calculating the displacement of an object, finding the distance traveled by a moving object, or determining the difference between two values in a data set. It is also used in physics to calculate the work done by a force over a certain distance.