Find a function p(t) which satisfies p"(t)=-sin(t), p(0)=1 and p(π)=(1+π).?
Find a function p(t) which satisfies p"(t)=-sin(t), p(0)=1 and p(π)=(1+π).
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Find a function p(t) which satisfies p"(t)=-sin(t), p(0)=1 and p(π)=(1+π).
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p"(t)=-sin(t),
p' = - cos t + c
p = -sin t + ct + d ------------------(1)
p(0) = 1 = -sin 0 + c(0)t + d
d = 1
p(π) = (1+π) = -sinπ + cπ+ d
(1+π) = 0+ cπ+ 1
c = 1
So p = -sin t + ct + d
Substitute c and d into (1)
It becomes p(t) = -sin t + t + 1