#int color(white)(.) sin(x^2)# ?

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Answer 1 · 2018-06-10T21:25:57

#int sin^2 """x"" " dx=x/2-(sin 2x)/4 + C#

The question is not so clear.

Just in case it means,

Integrate #(sin x)^2#, then

From Half-Angle Formulas in Trigonometry,

#sin^2 x=1/2-1/2cos 2x#

Integration part

#int sin^2 """x"" " dx=int (1/2-1/2cos 2x)dx#

#int sin^2 """x"" " dx=int (1/2)dx-1/2int(cos 2x)dx#

#int sin^2 """x"" " dx=int (1/2)dx-1/((2)(2))int(cos 2x)2dx#

#int sin^2 """x"" " dx=1/2x-1/4sin 2x+C#

I hope the explanation is useful.....God bless...