∫√(sinx-sin³x)dx (0→π)
= ∫√[sinx(1-sin²x)]dx (0→π)
= ∫√[sinxcos²x]dx (0→π)
= ∫cosx(√sinx)dx (0→½π) - ∫cosx(√sinx)dx (½π→π)
= ∫(√sinx)dsinx (0→½π) - ∫(√sinx)dsinx (½π→π)
= ⅔ (sinx)^(3/2)(0→½π) - ⅔ (sinx)^(3/2)(½π→π)
= ⅔(1 - 0) - ⅔(0 - 1)
= 4/3
∫√(sinx-sin³x)dx (0→π)
= ∫√[sinx(1-sin²x)]dx (0→π)
= ∫√[sinxcos²x]dx (0→π)
= ∫cosx(√sinx)dx (0→½π) - ∫cosx(√sinx)dx (½π→π)
= ∫(√sinx)dsinx (0→½π) - ∫(√sinx)dsinx (½π→π)
= ⅔ (sinx)^(3/2)(0→½π) - ⅔ (sinx)^(3/2)(½π→π)
= ⅔(1 - 0) - ⅔(0 - 1)
= 4/3