What is the integral from 0 to pi/2 of (cos(θ))/(sqrt(1+sin(θ))) ?

The integral from 0 to pi/2 of (cos(θ))/(sqrt(1+sin(θ))) is 2sqrt(2)-2

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integral from 0 to pi/2 of (cos(θ))/(sqrt(1+sin(θ)))

\int_{0}^{\frac{π}{2}} \frac{cos ( θ )}{1 + sin ( θ )} d θ

22 - 2

Decimal Notation

0.82842 \dots

Solution steps

\int_{0}^{\frac{π}{2}} \frac{cos ( θ )}{1 + sin ( θ )} d θ

Apply u-substitution

: \int_{1}^{2} \frac{1}{u} d u

= \int_{1}^{2} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{1}^{2}

= [2 u^{\frac{1}{2}}]_{1}^{2}

Apply radical rule:

= [2 u]_{1}^{2}

Compute the boundaries:

22 - 2

= 22 - 2

n = 0 \sum \infty 2 (\frac{- 2}{3})^{n}

\frac{d y}{d x} = e^{- (x + y)}

\int e^{- x + 2} d x

y = 4 (x + 1), y = 5 (x + 1), x = 5

f (x) = 9 sin (x) cos (x)

What is the integral from 0 to pi/2 of (cos(θ))/(sqrt(1+sin(θ))) ?
The integral from 0 to pi/2 of (cos(θ))/(sqrt(1+sin(θ))) is 2sqrt(2)-2