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As we saw in Section 3.8, a radioactive substance decays exponentially: The mass at time $ t $ is $ m(t) = m(0)e^{kt} $, where $ m(0) $ is the initial mass and $ k $ is a negative constant. The mean life $ M $ of an atom in the substance is$$ M = -k \int_0^\infty te^{kt}\ dt $$For the radioactive carbon isotope, $ ^{14} C $, used in radiocarbon dating, the value of $ k $ is $ -0.000121 $. Find the mean life of a $ ^{14} C $ atom.

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8264

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

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Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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As we saw in Section $3.8$…

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As we saw in Section $3.4,…

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As we saw in Section 3.8 ,…

09:40

As we saw in Section $3.8,…

05:14

As we saw in Section $6.5,…

03:38

Mean Life of Radioactive N…

01:52

The radioactive isotope ca…

07:08

$\quad$ When a radioactiv…

01:10

A radioactive sample has a…

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