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KataKoniK
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[tex]\int_{0}^{x} [t \int_{1}^{t} f(u)du] dt[/tex]
I don't know what to do. Thanks in advance
I don't know what to do. Thanks in advance
Last edited:
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is calculated by finding the slope of the tangent line to the curve at that point.
Finding the derivative of an integral allows us to determine the original function that was integrated. It also helps us to analyze the behavior of the function and make predictions about its future values.
The process for finding the derivative of an integral is known as the Fundamental Theorem of Calculus. It involves taking the derivative of the original function and evaluating it at the upper and lower limits of integration.
No, not all integrals have a known derivative. Some integrals may require advanced techniques such as substitution or integration by parts to find the derivative.
We can verify the correctness of our derivative by taking the integral of the derivative and comparing it to the original function. If the two are equal, then we have found the correct derivative.