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!

  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 ...

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

Then the integral becomes straightforward:

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Additional comment

The slightly messy algebra involves the identities ...

  (a+b)(a-b) = a² -b²

  (a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴

452,489 to the nearest thousand is 452,000

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98