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Evaluate the integral and interpret it as a difference of areas. Illustrate with a sketch.$\displaystyle \int^{2\pi}_{\pi/6} \cos x \,dx$

$$\int_{\pi / 6}^{2 \pi} \cos (x) d x=-\frac{1}{2}$$

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Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Michael J.

Idaho State University

Boston College

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Video Transcript

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.

Topics

Integrals

Integration

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp