Definite integral to indefine one

Thread starter chessmath
Start date Nov 1, 2012
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Definite integral Integral

In summary, a definite integral is a mathematical concept used to find the area under a curve on a graph. It is different from an indefinite integral in that it has specific limits of integration, giving a numerical value instead of a general function. The purpose of finding a definite integral is to calculate the area under a curve, which can be useful in real-world applications. To evaluate a definite integral, the indefinite integral must first be found and then the upper and lower limits of integration are plugged in and subtracted to get the final value. The definite integral and derivative are inverse operations, with the definite integral finding the total change over an interval and the derivative finding the instantaneous rate of change at a specific point.

Nov 1, 2012

chessmath

Hi
I would like to know what is the procedure to convert indefinite integral to definite one?
For example I know ∫exp(-u^2)du from 0 to x is equal to ∫x*exp(-x^2*t^2)dt from 0 to 1
But I would like to know with what type of change of variable I get these?

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Nov 1, 2012

lurflurf

Homework Helper

clearly
u=x t

FAQ: Definite integral to indefine one

What is a definite integral?

A definite integral is a mathematical concept used to find the area under a curve on a graph. It is represented by the symbol ∫ and is calculated by evaluating the function within the specified limits.

How is a definite integral different from an indefinite integral?

A definite integral has specific limits of integration, while an indefinite integral does not. This means that a definite integral gives a numerical value, while an indefinite integral gives a general function.

What is the purpose of finding a definite integral?

The purpose of finding a definite integral is to calculate the area under a curve, which can be useful in many real-world applications such as calculating distance, volume, and work done.

How do you evaluate a definite integral?

To evaluate a definite integral, you must first find the indefinite integral of the function. Then, plug in the upper and lower limits of integration and subtract the results to get the final value.

What is the relationship between the definite integral and the derivative?

The definite integral and the derivative are inverse operations of each other. This means that the definite integral finds the total change over a given interval, while the derivative finds the instantaneous rate of change at a specific point.