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Evaluate the given sum.$$\left.\sum_{j=1}^{4}(j i-1)+3\right)$$

$$32$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

Campbell University

Baylor University

University of Michigan - Ann Arbor

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.

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Mhm. Hello here we have the somewhere we have J going from 1 to 4 of J squared plus one. Um So comparing to some with some going from k from one to the end of a sub K. We see that we have a sub J is J squared plus one and is equal to four. So we get here is plugging in one at first we get one squared which is one plus one so that's two. And then and we were adding when J is too, so that's two squared is +44 plus one is five, so two plus five and then three squared is nine plus one is 10. And then when jay is four we get four squared is 16 plus one is 17. Just adding here two plus five plus 10 plus 17 And the sum is equal to 34.

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