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A nearby pond has 5 frogs, and the population doubles every year. The inequality 5(2)^t>75, where t is the number of years, m
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Replace :
Split the integral at x = 1, and consider the latter one over [1, ∞) in which we replace :
Then the original integral is equivalent to
Recall that for |x| < 1,
so that we can expand the integrand, then interchange the sum and integral to get
Integrate by parts, with
Recall the Fourier series we used in an earlier question [27217075]; if where 0 ≤ x ≤ 1 is a periodic function, then
Evaluate f and its Fourier expansion at x = 1/2 :
So, we conclude that