August 20, 2019, 12:53:26 pm

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#### georgebanis

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##### Trig Functions Question
« on: February 12, 2019, 06:48:13 pm »
0
Hey guys, would you know how to do part B of the question below. I have the answer to part A (√3/2) but just need a hand with the second part where the answer is (b) π/24(4π +3√3).

The region R is bounded by the curve y = cos2x, the x-axis and the lines x = π/6 and x = −π/6. (a) Sketch R and then ﬁnd its area. (b) Find the exact volume generated when the region R is rotated about the x-axis.

Thanks

#### AlphaZero

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##### Re: Trig Functions Question
« Reply #1 on: February 12, 2019, 07:17:41 pm »
+2
Hey guys, would you know how to do part B of the question below. I have the answer to part A (√3/2) but just need a hand with the second part where the answer is (b) π/24(4π +3√3).

The region R is bounded by the curve y = cos2x, the x-axis and the lines x = π/6 and x = −π/6. (a) Sketch R and then ﬁnd its area. (b) Find the exact volume generated when the region R is rotated about the x-axis.

Thanks

The volume of the specified region is given by $V=\pi\int_{-\pi/6}^{\pi/6}\cos^2(2x)\;dx.$Using double angle formulae, we can write this as $V=\frac{\pi}{2}\int_{-\pi/6}^{\pi/6}\Big(1+\cos(4x)\Big)\;dx,$ which should be easy to evaluate.
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#### RuiAce

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##### Re: Trig Functions Question
« Reply #2 on: February 12, 2019, 07:45:30 pm »
+2
The volume of the specified region is given by $V=\pi\int_{-\pi/6}^{\pi/6}\cos^2(2x)\;dx.$Using double angle formulae, we can write this as $V=\frac{\pi}{2}\int_{-\pi/6}^{\pi/6}\Big(1+\cos(4x)\Big)\;dx,$ which should be easy to evaluate.
Note that double angles are not in the 2u syllabus.

Having said that.
Hey guys, would you know how to do part B of the question below. I have the answer to part A (√3/2) but just need a hand with the second part where the answer is (b) π/24(4π +3√3).

The region R is bounded by the curve y = cos2x, the x-axis and the lines x = π/6 and x = −π/6. (a) Sketch R and then ﬁnd its area. (b) Find the exact volume generated when the region R is rotated about the x-axis.

Thanks
I can clearly see that Dan's method is correct, however this question was designed to be at the Extension 1 level. If it appeared in a 2U exam (and you weren't told to approximate it with say, Simpson's rule) then that is a mistake on their behalf. Otherwise, in the future, please post questions in the correct thread.