sin-x-dx-

Question Number 123133 by Khalmohmmad last updated on 23/Nov/20

\int \sqrt{\sin x} d x = ?

Commented by MJS_new last updated on 23/Nov/20

see question 84607

Commented by Dwaipayan Shikari last updated on 23/Nov/20

\sqrt{s i n x} = \sqrt{1 - {m s i n}^{2} θ}

1 - s i n x = {m s i n}^{2} θ

{(s i n \frac{x}{2} - c o s \frac{x}{2})}^{2} = {m s i n}^{2} θ

2 ({s i n}^{2} (\frac{x}{2} - \frac{π}{4})) = {m s i n}^{2} θ

θ = (\frac{x}{2} - \frac{π}{4}) m = 2

E (z ∣ m) = \int_{0}^{z} \sqrt{1 - {m s i n}^{2} x} d x

\int \sqrt{s i n x} d x = 2 E (\frac{x}{2} - \frac{π}{4} ∣ 2)