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If $ f(1) = 12 $, $ f' $ is continuous, and $ \displaystyle \int^4_1 f'(x) \, dx = 17 $, what is the value of $ f(4) $?
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00:42
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 3
The Fundamental Theorem of Calculus
Integration
Baylor University
University of Michigan - Ann Arbor
Idaho State University
Boston College
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.
00:38
If $f(1)=12, f^{\prime}$ i…
01:50
$$ \begin{array}{l}{\text …
02:20
0:00
Suppose that $ f(1) = 2 $,…
03:22
Suppose that $f(1)=2, f(4)…
01:27
$\begin{array}{l}{\text { …
okay. Given the fundamental theory cockles part to Rio the integral from A to B f of x d. X is off of Beamers off of Ed. Therefore, given the integral from 1 to 4 after prime of Axe DX, we know this is a government 17 which means that before come on, it's off of one is also equipment 17. We know everyone is actually 12 so let's not plug in what we know. This means that half of four is 17 post 12 so after four is 29.
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