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Problem 52 Hard Difficulty

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

$ y = \sec^2 x $, $ 0 \le x \le \pi/3 $

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Video Transcript

Okay, drying the graph. We know this shaded region as the area as we can see, We're looking at the integral from the bounds of 02 pi over three. Seek and squared acts. Detox is 10 acts 02 pi over three. Plug in now. Tan of pi over three, minus 10 of zero. A squirt of three months here, which is simply squirt of three, which matches up with a rough estimate over here. If you were to do one times approximately three and then half of that because we know this is one and this is three out. But remember, this is no a rectangle. It curved over here, and this matches up.