Question

Guys, please help.

$\huge \displaystyle \sf { \int_{0}^{ \frac{\pi}{3} }\frac{ {cos}^{2} x}{ \sqrt{1 + cos {}^{2} x} } \: dx }$

No spamming..!!​

Answer 1

I = da 0 1+ cos²x

(1)

I = (T-x).sin(T-x).dx 1 + cos² (π - x) 0

I (π - x).sinx.dx 1 + cos²x 0

On adding (1)&(2), we get

21 = xsinx + T sinx - xsinx 1 + cos²x 0 dx

21= sinx 1 + cos²x da

cosa = t

-sinx.dx = dt -1 I = dt

2 1 + t² -1 [tan ¹] ¹ I = 2

I = 2 [tan ¹(-1)-tan(1)]

I = -T 2 ㅠ

I = X

I 2