Mathematics: Use Wolframalpha to find the exact volume of the solid obtained by rotating about x = [pi]/2 the region bounded by y = sin^2x, y = sin^4x, x in [0,[pi]/2]. [Notation: c in [a,b] means a leq c leq b.]

Use Wolframalpha to find the exact volume of

Ответ:

ambercuevas2707

19.01.2022

Mathematics

Step-by-step explanation:

Here the region between two curves is rotated about a vertical line.

The functions are

$y = sin^2x, \\y = sin^4x, \\x in [0,[pi]/2].$

Intersecting points are x=0 and x =pi/2

Since rotated about x = pi/2 we get

using cylindrical shell method

Volume = $2\pi rh\\=2\pi \int\limits^\frac{\pi}{2} _0 {xy} \, dx \\=2\pi \int\limits^\frac{\pi}{2} _0 (x+\frac{\pi}{2} )(sin^2 x -sin^4 x) dx\\$

From wolfram alpha we find that

Volume= $2\pi (\frac{3\pi^2 }{64)} =\frac{6\pi^3}{64}$

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Ответ:

cacaface311

25.02.2020

Mathematics

Step-by-step explanation: divide $2.50 by 2 then leave answer alone for a minute. Then convert 1 1/4 into fraction and divide it by $3.25 and the two answers you get subtract it with each other and that will be the answer!

*follow these steps and see if you get a reasonable answer* (these steps are right believe me)

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Use Wolframalpha to find the exact volume of the solid obtained by rotating about x = [pi]/2 the region bounded by y = sin^2x, y = sin^4x, x in [0,[pi]/2]. [Notation: c in [a,b] means a leq c leq b.]

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