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Have you heard of the binomial theorem? For the first problem, I make the substitution u= cos(x) which implies du = -sin(x)dx and after using the fact that m=2013 is odd and sin(x)^2= 1-cos(x)^2 I can get the integrand to be:
But from here the...
The perimeter P of a rectangle is twice the length L plus twice the width W. As an equation this is:
P = (2 x L) + (2 x W)
You are given that the rectangle is 1/2 mile long, so L = 1/2 mi, and it is 1/4 mile wide, so W = 1/4 mi.
Plugging these values for L and...