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Integral

How do you solve this integral in the domain shown? Please show each step.

domain: ½ ≤ t ≤ 1

∫ 6dt ∕ √(3 + 4t - 4t²)

Solution This solution is FREE courtesy of BrainMass!

∫ 6dt ∕ √(3 + 4t - 4t²)=∫ 6dt ∕ 2√(1-(t²-t+0.25))=∫ 3dt ∕ √(1-(t²-t+0.25)) then y=t-0.5 we get
∫ 3dy ∕ √(1-y²)= 3 arc sin (y) and now we should change the integral limits using the y=t-0.5.
y=0.5-0.5=0 lower
y=1-0.5 upper

and integral is equal to 3 arcsin(1)-3 arcsin(.5)