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t∈[0,infinity]-----------(1)

and the domain of x in sin function is -π/2 to +π/2 so domain of sin4t will be

-π/2 ≤ 4t ≤ +π/2-------(A)

-π/8 ≤ t ≤ π/8

so it will be t∈[-π/8,+π/8]---------(2)

so the common will be t ∈[0,π/8]

now put the values 0 and π/8 in the equation

we will get

t=0 so the equation will be equals to zero

t=π/8 the answer will be π^2/64

or you can simply the values of - and + π/2 in the step (A)