Monday, December 27, 2021

12 Days of Christmas Integrals: ∫ (sin(x))^2 dx

 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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