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Evaluate the integral and interpret it as a difference of areas. Illustrate with a sketch.

$ \displaystyle \int^{2\pi}_{\pi/6} \cos x \,dx $

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01:29

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Missouri State University

Oregon State 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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Evaluate the integral and …

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Use Part 2 of the Fundamen…

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Sketch the region of integ…

Okay. The integral from pi. Over six to pie, Of course. Sign Axe Detox we know is sine X. And then we have our bounds plug in Sign of two pi, which we know is zero minus sign of plow over six, which we know is 1/2 0 minus 1/2 is negative 1/2. This is our solution. And then to illustrate this.

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