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Evaluate the given sum.$$\sum_{i=1}^{20} 12$$

$$240$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

Baylor 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.

00:58

Evaluating a Sum Find the …

01:07

01:32

Find and evaluate the sum.…

00:20

Evaluate the sum.$\sum…

01:16

all right, we have a slightly easier summation to have here. The reasons he's here is because there's no variable here. That means there's no four or five or six all the way up to 12. There's nothing really to substitute in. And so this literally means 10 is gonna be the term every single time. And so we can just kind of be careful and say, OK, I have to add up The fourth term to the 12th term Mother is the fourth six, and I'm not gonna write all these out. I can kind of use in math as a shortcut, say 12 minus four is eight and, well, might be tempting to say, Oh, there's gonna be eight of these tens. There's actually gonna be nine of them. And the reason there's nine is because if you include four and 12 there ends up being one extra one in there, so there's gonna be nine tens in there and nine times 10 obviously, is 90. There is your summation

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