Activity › Discussion › Math › Integral of sin2x › Reply To: Integral of sin2x

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The integral of sin^2(x) with respect to x can be computed using various trigonometric identities and integration techniques. One approach is to use the double angle identity for sine, which states that sin(2θ) = 2sin(θ)cos(θ). Applying this identity to sin^2(x), we have:
sin^2(x) = (1/2)(1 – cos(2x)).
Now, we can integrate term by term:
∫sin^2(x) dx = ∫(1/2)(1 – cos(2x)) dx
= (1/2) ∫(1 – cos(2x)) dx
= (1/2)(x – (1/2)sin(2x)) + C,where C is the constant of integration.
Therefore, the integral of sin^2(x) is (1/2)(x – (1/2)sin(2x)) + C, where C is a constant.