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Let $ f(0) = 0 $ and $ f(x) = 1/x $ if $ 0 < x \le 1 $. Show that $ f $ is not integrable on $ [0, 1] $. [$ Hint: $ Show that the first term in the Riemann sum, $ f(x_i^*) \Delta x $, can be made arbitrarily large.]

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02:04

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

University of Michigan - Ann Arbor

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.

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We know that if and it's the number of rectangles in the width of the wrecked tank would be Delta Acts is one minus here, over on which is one over an There for the area of the first rectangle would simply be, and therefore we know we have the sum from aye equals one. Don't forget the limit. We know this is greater than the limit. As UN approaches, infinity on equals infinity as you can see the first term and some go to infinity. So it's not Integra ble on a certain interval if it goes towards positive or negative infinity. Therefore there's no limit, so it's not in terrible on this interval 01

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