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Find the average of (a) the first 99 integers, (b) the first 999 integers, (c) the first $n$ integers.

(a) 50(b) 500(c) $\frac{n+1}{2}$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

Missouri State University

Baylor University

University of Nottingham

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.

00:45

Find three arithmetic mean…

01:35

To find the sum of the fir…

01:15

Find each sum as described…

02:12

Find the mean of the follo…

00:54

Find the mean (average) of…

02:16

To find the average (mean)…

Here is a list of numbers:…

03:03

we want an insert. Three numbers in between 99 100 so that it forms an arithmetic sequence. So one, 234 were adding four unknowns will call exes to go from 99 to 100. Um, so really were saying 99 plus four X is equal to 100 moving on 99 over. That'll give before X equals one. So X is equal to 1/4. So each time we're adding 1/4 to it, it'll be 99 1/4 uh, 99 2/4 which is just 1/2 99 and 3/4. 99. 4/4 is 100. So this is the sequence that we're looking for.

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