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Numerade Educator

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Problem 54 Medium Difficulty

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

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

Answer

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

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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.