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While we gave only three simple formulas for computing sums, there are many more in your calculator's memory. Use your calculator to compute each of the following sums.$$\sum_{j=1}^{18}\left(2+5 j^{2}-3 j^{5}\right)$$

$$-19,961,022$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

University of Nottingham

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.

00:53

Evaluating a Sum Use a gra…

00:20

04:12

In the following exercises…

02:02

All right. So another problem where you just kind of have to plug it into your calculator. And if yours is like mine in that when you try to plug it in, it makes this an and automatically make sure you plug in an end automatically for the term. Make sure limits are five for your lower limit and 15 for your upper limit. And thank goodness that you're calculator can do this because this is truly one of the more complex, an ugly fractions I've ever seen so ugly that just decided to hide it. Initially, that fraction is so large and complex that I'm just writing it here. But the reason it's most likely this complex is because if you can imagine squaring 15 and then adding one, all the common denominators I would need to be added would create this nasty, nasty fraction here. But there is your answer that you did not have to calculate yourself. Luckily,

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