20 points for a definite integral calculation process, hope to be more detailed ∫ lower limit 0, upper limit Π / 2 (1-cos ^ 4 θ) d θ the answer is 5 Π / 4

20 points for a definite integral calculation process, hope to be more detailed ∫ lower limit 0, upper limit Π / 2 (1-cos ^ 4 θ) d θ the answer is 5 Π / 4

∫ lower limit 0, upper limit Π / 2 (1-cos ^ 4 θ) d θ = ∫ (1-cos ^ 2 θ) (1 + cos ^ 2 θ) d θ = ∫ (sin ^ 2 θ) (1 + cos ^ 2 θ) d θ = ∫ ((sin ^ 2 θ) + (sin θ cos θ) ^ 2) d θ = ∫ ((1 / 2) (1-cos2 θ) + (1 / 4) (sin2 θ) ^ 2) d θ = ∫ ((1 / 2) - (1 / 2) Cos2 θ + (1 / 8) (1-cos4 θ

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