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Use a graphing utility, where helpful, to find the area of the region enclosed by the curves.$$y=\sin x, y=\cos x, x=0, x=2 \pi$$

$$4 \sqrt{2}$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 6

APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

Section 1

Area Between Two Curves

Integrals

Integration

Applications of Integration

Area Between Curves

Volume

Arc Length and Surface Area

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Okay, Um So when heading, use a graphing calculator to show you, Um, the sign curve is the red one. That co sign curve is a black one. The vertical line x equal zero in the vertical lines. X equals two pi eso as you're looking at this, what you have to be careful with if you're not using a graphing calculator, is you want to make sure that you do co sign minus sign from zero to pi over four and then switch over Teoh do sign minus co sign from pirate for 25 pi over four and then switch back to co sign a minus sign from five power for 22 pi because that's where they want you to stop. Otherwise, if you're using a calculator, you can just, you know, find your function that has the in a role from zero to too high the way. This is where you find the high value in this calculator and what you want to do then is so you only have to do. One function is if you just do the absolute value, um, and makes everything positive. Um, now, the downside to this calculators, it does not give you an exact answer. Um, but if you checks with an exact answer and some calculus actually might let you get an exact answer, I have not seen this capability. It is exactly four route to, um But if you actually went through the process and you did zero to pi over four pi over 4 to 55 R four, then 5/4 to 2 pi and worked it allowed by hand finding values on the unit circle, you'll get exactly that. Makes perfect sense for root twos. Your answer, by the way.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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