Mathematics, 21.02.2022 09:20 austintules2005

Hello everyone, I'm just having trouble on a question for my Calculus work. Does anyone know where to start with this problem? Any help would be greatly appreciated!

Hello everyone, I'm just having trouble on a question for my Calculus work. Does anyone know where

Answers: 2

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Answer from: privise

sin(8w)/1024 -sin(4w)/128 +3w/128

Step-by-step explanation:

No doubt there are a variety of formulas and identities that can be used. Absent knowledge of those, I found it convenient to rewrite the integrand using Euler's formula. It tells you ...

$\sin(x)=\dfrac{e^{ix}-e^{-ix}}{2i},\quad\cos(x)=\dfrac{e^{ix}+e^{-ix}}{2}$

After some only slightly messy algebra, we find ...

$\cos^4(w)\sin^4(w)=\dfrac{\cos(8w)-4\cos(4w)+3}{128}$

Then the integral becomes straightforward:

$\displaystyle \int{\cos^4(w)\sin^4(w)}\,dw=\int{\dfrac{\cos(8w)}{128}}\,dw-\int{\dfrac{\cos(4w)}{32}}\,dw+\dfrac{3}{128}\int{}\,dw\\\\=\boxed{\dfrac{\sin(8w)}{1024}-\dfrac{\sin(4w)}{128}+\dfrac{3w}{128}}$

Additional comment

The slightly messy algebra involves the identities ...

(a+b)(a-b) = a² -b²

(a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴

Answer from: Quest

answer: 38.47 is your answer

step-by-step explanation: hope i you and who ever sees this answer have a great rest of your day : )

Answer from: Quest

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total value of u.k. shipments for

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(continued on page 79)

step-by-step explanation:

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