Question 2)iii)

Submitted by Anonymous (not verified) on

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For the x = sin^2(θ) substitution I've used the original In (given at the beginning of the question), but I keep getting pi/4 instead of pi/8 as the value of I(0.5). Before integrating with respect to θ, my integral simplifies to 0.5. Is this correct?

I think it's slightly different

Submitted by Rayman (not verified) on

Should get $\dfrac 14 \int ^{\pi / 2} _0 (1 - \cos (4 \theta) ) \mathrm d \theta$
I think.