12 Days of Christmas Integrals: ∫ (sin(x))^2 dx
On the Third day of Christmas Integrals, the integral featured today is...
∫ (sin(x))^2 dx
This calls for the trig identity:
(sin(x))^2 = 1/2 - 1/2 ∙ cos(2 ∙ x)
With any operations in calculus involving trigonometric functions, the angle units are assumed to be in radians.
∫ (sin(x))^2 dx
= ∫ 1/2 - 1/2 ∙ cos(2 ∙ x) dx
= 1/2 ∙ x - 1/4 ∙ sin(2 ∙ x) + C
= 1/2 ∙ x - 1/2 ∙ sin(x) ∙ cos(x) + C
Simple as that. We will get meatier integrals as the days wear on.
Eddie
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