$\int . sin (x^{2})$ $int color(white)(.) sin(x^2)$ ?

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Answer 1 · 2018-06-10T21:25:57

$\int {sin}^{2} x d x = \frac{x}{2} - \frac{sin 2 x}{4} + C$ $int sin^2 """x"" " dx=x/2-(sin 2x)/4 + C$

The question is not so clear.

Just in case it means,

Integrate ${(sin x)}^{2}$ $(sin x)^2$ , then

From Half-Angle Formulas in Trigonometry,

${sin}^{2} x = \frac{1}{2} - \frac{1}{2} cos 2 x$ $sin^2 x=1/2-1/2cos 2x$

Integration part

$\int {sin}^{2} x d x = \int (\frac{1}{2} - \frac{1}{2} cos 2 x) d x$ $int sin^2 """x"" " dx=int (1/2-1/2cos 2x)dx$

$\int {sin}^{2} x d x = \int (\frac{1}{2}) d x - \frac{1}{2} \int (cos 2 x) d x$ $int sin^2 """x"" " dx=int (1/2)dx-1/2int(cos 2x)dx$

$\int {sin}^{2} x d x = \int (\frac{1}{2}) d x - \frac{1}{(2) (2)} \int (cos 2 x) 2 d x$ $int sin^2 """x"" " dx=int (1/2)dx-1/((2)(2))int(cos 2x)2dx$

$\int {sin}^{2} x d x = \frac{1}{2} x - \frac{1}{4} sin 2 x + C$ $int sin^2 """x"" " dx=1/2x-1/4sin 2x+C$

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

∫.sin(x2)int color(white)(.) sin(x^2) ?