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A pd f is given by the equation $f(x)=\frac{1}{16}(8-2 x)$ over the interval [0,4](a) Verify that $f$ is a $p d f$ and (b) determine $\operatorname{Pr}(1 \leq x \leq 3).$

(b) $1 / 2$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

Campbell University

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.

01:39

If $f^{\prime}(x) \leq 2$ …

00:43

01:28

If $f(x)=\left\{\begin{arr…

01:25

04:35

So in this instance it is saying that um F of zero is 1. F of zero is one. So I'm going to say this is 1234 Mhm. And the derivative Is always less than or equal to two On the interval 0- three. So the slope Is always less than or equal to two. So if the slope was true to it would go up, Rise to run one, Rise to run one, it would be going up way, way up. Half of three is less than four, that's way below that line. So it could really be anything below this line, It could be anywhere below this line. Um So the statement is false.

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