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A continuous money flow begins at $\$ T_{0}$ and increases exponentially at a continuous rate $j$ per year for $t$ years. Find the present value if money is worth $r$ compounded continuously.

$T_{0}\left[\frac{e^{(j-r) t}-1}{j-r}\right]$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

Oregon State University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

04:02

Find the future value at a…

10:57

Accumulated Amount of Mone…

01:10

03:39

If $P$ dollars are left in…

08:10

Money Flow The rate of a c…

01:06

Find the accumulated futur…

02:21

01:36

If an initial amount $ A_0…

01:34

Accumulated present value.…

03:25

find the present value $P$…

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